Volume-6 , Issue-1 , Feb 2019, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  A Study on Factors Related to Southwest Monsoon Rainfall: A Microscopic Approach.

  K. S. Bhanu, A. R. Pali, D. P. Tadke

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.94-104, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.94104

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  Abstract
  Southwest monsoon rainfall has an undeviating effect on Indian economy. Different climatic conditions across India affect the monsoon at different places in different ways. Hence, it becomes important to study the factors related to the monsoon rainfall at a microscopic level. Our study concentrates on Nagpur, the geographical centre of India. In this paper we have found that the onset date of southwest monsoon in Nagpur city is not uniformly distributed over the month of June by using Chi-square goodness of fit test. An interesting result about the interconnectivity between arrival of heat wave and southwest monsoon is obtained using Chi-square test of independence. The relation between evapotranspiration and ground water level is also explored. It is found that the type of vegetation at a place majorly affects its ground water level. Multiple Linear Regression is also used to find the factors significantly affecting the amount of precipitation in the region and established a model for future rainfall prediction.

  Key-Words / Index Term
  Southwest monsoon, Chi-square goodness of fit test, Chi-square test of independence, Ground water level, Evapotranspiration, Multiple Linear Regression, Precipitation

  References
  [1]. P. Goswami, K. C. Gouda, “Objective Determination of the Date of Onset of Monsoon Rainfall over India based on Duration of Persistence”, CSIR Centre for Mathematical Modelling and Computer Simulation, Research Report RR CM 0711, June 2007.
  [2]. D. S. Pai, M. Rajeevan, “Indian Summer Monsoon Onset: Variability and Prediction”, National Climate Centre, Research Report No: 4/2007, October 20017.
  [3]. P. Guhathakurta, Elizabeth Saji,” Trends and variability of monthly, seasonal and annual rainfall for the districts of Maharashtra and spatial analysis of seasonality index in identifying the changes in rainfall regime”, National Climate Centre, Research Report No: 1/2012, May 2012.
  [4]. Tam Tze Huey, Ab Latif Ibrahim,”Statistical Analysis of Annual Rainfall Patterns in Peninsular Malaysia Using TRMM Algorithm”, In the Proceedings of the 33rd Asian Conference on Remote Sensing 2012, ACRS 2012.
  [5]. D. T. Deshmukh, H. S. Lunge, “Impact of Global Warming on Rainfall,And Cotton Lint with Vulnerability Profiles of Five Districts In Vidarbha, India”, International Journal of Scientific & Technology Research, Vol. 1, Issue-11, pp. 77-85, 2012.
  [6]. Abdul Haleem A. Al-Muhyi, Abather J. Bashar, Aymen Abdullateef Kwyes, “The Study of Climate Change Using Statistical Analysis Case Study Temperature Variation in Basra”, International Journal of Academic Research, Vol.3, Issue-2(5), pp. 10-23, 2016.
  [7]. R. Sukanya and K. Prabha, “Comparative Analysis for Prediction of Rainfall using Data Mining Techniques with Artificial Neural Network”,International Journal of Computer Sciences and Engineering, Vol. 5, Issue-6, pp. 288-292, 2017.
  [8]. T. Tammets ,“Estimation of extreme wet and dry days through moving totals in precipitation time series and some possibilities for their consideration in agrometeorological studies”, Agronomy Research, Vol. 8, Issue-2,pp. 433–438, 2010.
  

  Citation
  K. S. Bhanu, A. R. Pali, D. P. Tadke, "A Study on Factors Related to Southwest Monsoon Rainfall: A Microscopic Approach.," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.94-104, 2019

• Open Access   Article

  On Weighted Sushila Distribution with Properties and its Applications

  A. A. Rather, C. Subramanian

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.105-117, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.105117

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  Abstract
  In this paper, we have proposed a new version of Sushila distribution known as weighted Sushila distribution. The weighted Sushila distribution has three parameters. The different structural properties of the newly model have been studied. The maximum likelihood estimators of the parameters and the Fishers information matrix have been discussed. Finally, a real life data set has been analyzed, where it is observed that weighted Sushila distribution has a better fit compared to Sushila distribution.

  Key-Words / Index Term
  Weighted distribution, Sushila distribution, Reliability analysis, Maximum likelihood estimator, Order statistics, Entropies, Likelihood ratio test

  References
  [1] Alshkaki, R. S. A. (2016) An Extension to the Zero-Inflated Generalized Power Series Distributions, International Journal of Mathematics and Statistics Invention, vol. 4, no. 9, pp. 45-48.
  [2] Borah, M. and Hazarika, J. (2018) Poisson-Sushila distribution and its applications, International Journal of Statistics & Economics, 19(2), pp. 37-45.
  [3] Cox D. R. (1969). Some sampling problems in technology, In New Development in Survey Sampling, Johnson, N. L. and Smith, H., Jr .(eds.) New York Wiley- Interscience, 506-527.
  [4] Dey, S., Ali, S., & Park, C. (2015). Weighted exponential distribution: properties and different methods of estimation. Journal of Statistical Computation and Simulation, 85(18), 3641-3661.
  [5] Elgarhy, E. and Shawki, A. W. (2017) Exponentiated Sushila distribution, International Journal of Scientific Engineering and Science, 1(7), pp. 9-12.
  [6] Elgarhy, E. and Shawki, A. W. (2017) Kumaraswamy Sushila distribution, International Journal of Scientific Engineering and Science, 1(7), pp. 29-32.
  [7] Fisher, R. A. (1934), The effects of methods of ascertainment upon the estimation of frequencies. Annals of Eugenics, 6, 13-25.
  [8] Fuller, E. J., Frieman, S., Quinn, J., Quinn, G., and Carter, W. (1994): Fracture mechanics approach to the design of glass aircraft windows: A case study, SPIE Proc 2286, 419-430
  [9] Khan, M. N., Saeed, A., & Alzaatreh, A. (2018). Weighted Modified Weibull distribution. Journal of Testing and Evaluation, 47(5), 20170370.
  [10] Kilany, N. M. (2016). Weighted Lomax distribution. SpringerPlus, 5(1). doi:10.1186/s40064-016-3489-2.
  [11] Rao, C. R. (1965), On discrete distributions arising out of method of ascertainment, in classical and Contagious Discrete, G.P. Patiled; Pergamum Press and Statistical publishing Society, Calcutta. 320-332.
  [12] Rather, A. A. and Subramanian, C. (2018) Characterization and Estimation of Length Biased Weighted Generalized Uniform Distribution, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.72-76.
  [13] Rather, A. A., Subramanian, C., Shafi, S., Malik, K. A., Ahmad, P. J., Para, B. A. and Jan, T. R. (2018), A new Size Biased Distribution with applications in Engineering and Medical Science, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.75-85.
  [14] Rather, A. and Subramanian, C., (2018), Length Biased Sushila distribution, Universal Review, vol. 7. No. XII, pp, 1010-1023.
  [15] Saratoon, A. (2017) Poisson –Sushila distribution and its application, B.Sc.(Applied Statistics) Research Project, Suan Sunandha Rajabhat University, Thailand,.
  [16] Shanker, R., Shambhu S., Uma S. and Ravi S., (2013) Sushila distribution and Its application to waiting times data, International Journal of Business Management, vol. 3, no. 2 , pp. 1-11.
  [17] Tsallis, C. (1988), Possible generalization of boltzmann-gibbs statistics. Journal of Statistical Physics, 52, 479-487.
  [18] Zelen, M. (1974). Problems in cell kinetic and the early detection of disease, in Reliability and Biometry, F. Proschan & R. J. Sering, eds, SIAM, Philadelphia, 701-706.
  

  Citation
  A. A. Rather, C. Subramanian, "On Weighted Sushila Distribution with Properties and its Applications," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.105-117, 2019

• Open Access   Article

  Role of Statistics in Mathematical Modeling

  S.K. Kalra

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.118-121, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.118121

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  The use of numerical model dependent on measurements is broadly utilized in numerous fields, particularly in assessment subject. In this paper have three sections Mathematical Modeling, Statistics and other is job of insights in Mathematical Modeling. Essentially both are parts of Mathematics Statistical and numerical displaying is critical to portray, decipher, think about and anticipate the conduct of complex frameworks. Insights and Mathematical models can be in numerous structures, including differential conditions, or theoretic models for precedents connection between`s hypothetical numerical models and test estimations. Mathematical Modeling gives the frame work to the complex problem and statistics analysis the problem, implementing the method and then concludes the result. In this paper we built up a numerical model for various masses design for temperamental state conditions and applying factual techniques for finding the arrangement.

  Key-Words / Index Term
  Mathematical Modeling, Statistical Method

  References
  [1] http://www.npl.co.uk/mathematics-scientific-computing/modelling/mathematical-and-statistical-modelling/
  [2] https://www.quora.com/What-is-the-relationship-between-statistics-and-mathematics
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  [5] https://www. onlinejournal.in/IJIRV319/092pdf
  [6] https://www.stetson.edu
  

  Citation
  S.K. Kalra, "Role of Statistics in Mathematical Modeling," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.118-121, 2019

• Open Access   Article

  An Optimum Sample Size in Cross Sectional Studies

  J. Sreedharan, S. Chandrasekharan, A. Gopakumar

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.122-130, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.122130

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  Sample size plays a vital role in any research as very less sample and very large sample may lead to false conclusions. There are many formulas available for the calculation of sample size according to the design of the study or/and statistical tool. These formulas generally give a minimum sample size but not provide solution for finding the required upper limit. Studies which include large sample give estimates with higher precision but may lead to large sample fallacy with statistical significance even for insignificant effects. This paper aimed to develop a formula for optimum sample size in the context of cross sectional study design. Pattern of changes in the results at minimum, optimum, large and extreme large sample size is discussed. Also we compare the result of cross sectional study with the result of a case control study. This study observed that an additional factor (m-factor) to be multiplied with the existing formula, that gives an optimum large sample in a cross-sectional study. The m-factor is a function of Zα and Zβ.

  Key-Words / Index Term
  Minimum sample size, Optimum sample size, Large sample size, Cross sectional study, Power

  References
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  [7] J. Charan, T. Biswas, “How to Calculate Sample Size for Different Study Designs in Medical Research?”, Indian Journal of Psychological Medicine, Vol.35,Issue.2,pp.121-126, 2013.
  [8] M.S. Setia, “Methodology Series Module 3: Cross-sectional Studies”, Indian Journal of Dermatology, Vol.61,Issue.3,pp.261-264, 2016.
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  [14] T.J. Naduvilath, R.K. John, L. Dandona, “Sample size for ophthalmology studies”, Indian Journal of Ophthalmology, Vol.48,Issue.3,pp.245-50, 2000.
  [15] S.B. Hulley, S.R. Cumming, W.S. Browner, D. Grady, N. Hearst, T.B. Newman. “Designing Clinical Research”, 2nd ed., Lippincot Williams & Wilkins, Philadelphia, USA, 2001.
  [16] R.B Dell, S. Holleran, R. Ramakrishnan, “Sample Size Determination”, Institute for Laboratory Animal Research Journal, Vol.43,Issue.4,pp.207-213, 2002.
  [17] D.J. Biau, S. Kerneis, R. Porcher, “Statistics in brief: The importance of sample size in the planning and interpretation of medical research”, Clinical Orthopaedics and Related Research, Vol.466,Issue.9,pp.2282–8, 2008.
  [18] P. Kadam, S. Bhalerao, “Sample size calculation”, International Journal of Ayurveda Research, Vol.1,Issue.2,pp.55-57, 2010.
  [19] P. Bacchetti, “Current sample size conventions: Flaws, harms, and alternatives”, BMC Medicine, Vol.8,Issue.17, 2010.
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  Citation
  J. Sreedharan, S. Chandrasekharan, A. Gopakumar, "An Optimum Sample Size in Cross Sectional Studies," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.122-130, 2019

• Open Access   Article

  Comparison of Process Capability Indices under AR (2) process

  M. M. Deshpande, V. B. Ghute

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.131-137, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.131137

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  Abstract
  Statistical Process Control (SPC) tools are applicable in all fields. Process Capability Analysis (PCA) is one of the essential SPC tools. In Process Capability, it measures the ability of an in-control process to produce the desired product. Process Capability Indices (PCIs) are defined to measure the capability of the process. Along with in control process PCIs also assumes that the process characteristic is Normally distributed and the observations on characteristic are independent. The assumption of independent observations has violated in many industrial processes. The present paper focuses on the effect of this violation of independence which is also known as autocorrelation effect. ARMA models are appropriate for autocorrelated processes.

  Key-Words / Index Term
  Autocorrelated process, Estimation, Process Capability Indices (PCIs), Statistical Process Control

  References
  [1] S. Kotz, and N. L. Johnson, “Process Capability Indices – A Review, 1992-2000 Discussions”, Journal of Quality Technology, Vol 34, Issue 1, pp. 2–19, 2002
  [2] H. Shore, “Process Capability Analysis when Data are Autocorrelated”, Quality Engineering, Vol. 9, Issue 4, pp. 615–626, 1997.
  [3] N. F. Zhang, “Estimating Process Capability Indexes for Autocorrelated Data”, Journal of Applied Statistics, Vol. 25, Issue 1, pp. 559–574, 1998.
  [4] R. D. Guevara, and J. A. Vargas, “Comparison of Process Capability Indices under Autocorrelated Data”, Revista Colombiana de Estadística, Vol. 30, Issue 2, pp. 301-316, 2007.
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  Citation
  M. M. Deshpande, V. B. Ghute, "Comparison of Process Capability Indices under AR (2) process," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.131-137, 2019

• Open Access   Article

  Evaluation of Sampling Inspection Plans for Life-tests Based on Generalized Gamma Distribution

  R. Vijayaraghavan, K. Sathya Narayana Sharma, C. R. Saranya

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.138-146, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.138146

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  Abstract
  Acceptance sampling is concerned with rules for deciding about the acceptance or rejection of a lot of products submitted for inspection based on the quality of the products assessed through the testing of items drawn randomly from the lot. Sampling inspection plans which are used for taking decisions about the acceptability of the product with respect to life time are called life-test sampling plans. Lifetime of the product is considered as a continuous random variable, which is modelled by a probability distribution. The literature of sampling inspection for lifetime data provides applications of various types of continuous distributions in the studies relating to the design and evaluation of life-test sampling plans. This paper presents the procedures and tables for the selection of life-test sampling plans under the conditions for application of the generalized gamma distribution. The criteria for designing life-test plans when lot quality is evaluated in terms of mean life and hazard rate are proposed.

  Key-Words / Index Term
  Acceptable mean life, Hazard rate, Generalized Gamma Distribution, Mean life, Reliability sampling

  References
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  [37] United States Department of Defense, Sampling Procedures and Tables for Life and Reliability Testing Based on the Weibull Distribution (Reliability Life Criterion), Quality Control and Reliability Technical Report (TR 6), Office of the Assistant Secretary of Defense Installation and Logistics), U. S. Government Printing Office, Washington D. C., 1963.
  [38] United States Department of Defense, Factors and Procedures for Applying MIL-STD-105D Sampling Plans to Life and Reliability Testing, Quality Control and Reliability Assurance Technical Report (TR 7), Office of the Assistant Secretary of Defense (Installations and Logistics), Washington D. C., 1965.
  [39] Vijayaraghavan, R., Chandrasekar, K., and Uma, S. Selection of Sampling Inspection Plans for Life-test Based on Weibull - Poisson Mixed Distribution, Frontiers of Statistics and its Applications, Bonfring, Coimbatore, India, pp.225 - 232, 2012.
  [40] Vijayaraghavan, R., and Uma, S. Evaluation of Sampling Inspection Plans for Life Test Based on Exponential - Poisson Mixed Distribution, Frontiers of Statistics and its Applications, Bonfring, Coimbatore, India, pp.233 - 240, 2012.
  [41] Vijayaraghavan, R., and Uma, S. Selection of Sampling Inspection Plans for Life Tests Based on Lognormal Distribution, Journal of Testing and Evaluation, Vol.44,pp.1960 - 1969, 2016.
  [42] Wu, J. W., and Tsai, W. L. Failure Censored Sampling Plan for the Weibull Distribution, Information and management Sciences, Vol.11,pp.13 - 25, 2000.
  [43] Wu, J. W., Tsai, T. R., and Ouyang, L. Y. Limited Failure-Censored Life Test for the Weibull Distribution, IEEE Transactions on Reliability, Vol.50, pp.197 - 111, 2001.
  

  Citation
  R. Vijayaraghavan, K. Sathya Narayana Sharma, C. R. Saranya, "Evaluation of Sampling Inspection Plans for Life-tests Based on Generalized Gamma Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.138-146, 2019

• Open Access   Article

  Solution of European Call Option by the First Integral Method

  M. P. Ghosh, R. M. Gor

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.6 , Issue.1 , pp.147-154, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.147154

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  Abstract
  For finding the value of an option we use the widely used Black-Scholes formula in option pricing theory. In this paper, we convert the Black-Scholes PDE into ODE with boundary condition by using the First Integral Method and get accurate solution of Black-Scholes equation. Primarily, we address an error in a previously published work of other authors. We also show with numerical examples the effect of improved solution.

  Key-Words / Index Term
  Black-Scholes equation, First integral method, European call option

  References
  [1] A. Shinde,K.Takale, “Study of Black-Scholes Model and its Applications”, Procedia Engineering, Vol.38, pp.270-279, 2012.
  [2] Y.Saedi, G.Tularam,“AReview of the Recent Advances Made in the Black-Scholes Models and Respective Solutions Methods”, Journal of Mathematics and Statistics, Vol.14, Issue.1, pp.29-39, 2018.
  [3] F. Mehrdoust, M. Mirzazadeh, “On Analytical Solution of the Black-Scholes Equation by the First Integral Method”, UPB Sci. Bull., Series A, Vol.76, Issue.4, pp.85-90, 2014.
  [4] F.Rouah,“Four Derivations of the Black-Scholes PDE”, FRouah.com, Volopta.com,2011.
  [5] S.Park, J.Kim,“Homotopy analysis method for option pricing under stochastic volatility”, Applied Mathematics Letters, Vol.24, Issue.10, pp.1740-1744, 2011.
  [6] Aghajani, M.Ebadattalab,“The reduced differential transform method for the Black-Scholes pricing model of European option valuation”, Int. J. Adv. Appl. Math. and Mech., Vol.3, Issue.1, pp.135 – 138, ISSN: 2347-2529, 2015.
  [7] Z. Feng, “The first-integral method to study the Burgers–Korteweg–de Vries equation”, Journal of Physics A: Mathematical and General, Vol.35, Issue.2, pp.343-349, 2002.
  [8] F. Tascan, A. Bekir, M. Koparan, “Travelling wave solutions of nonlinear evolution equations by using the first integral method”, Communications in Nonlinear Science and Numerical Simulation, Vol.14, Issue.5, pp.1810-1815, 2009.
  [9] N. Taghizadeh, M. Mirzazadeh, A. SamieiPaghaleh., “The first-integral method applied to the Eckhaus equation”, Applied Mathematics Letters, Vol.25, Issue.5, pp.798-802,2012.
  [10] M. Bohner, Y. Zheng, “On analytical solutions of the Black–Scholes equation”, Applied Mathematics Letters, Vol.22, Issue.3, pp.309-313, 2009.
  [11] M. El-Sabbagh, S. El-Ganaini. “The first integral method and its applications to nonlinear equations”, Applied Mathematical Sciences, Vol.6, Issue.77-80, pp.3893-3906,2012.
  [12] V. Glkac,“The homotopy perturbation method for the BlackScholes equation”, Journal of Statistical Computation and Simulation,Vol.80, pp.1349-1354, 2010.
  [13] J. C. Hull, “Options, Futures, and Other Derivatives”, New Jersey: Prentice-Hall, USA, 1999.
  [14] K. Raslan, “The first integral method for solving some important nonlinear partial differential equations”, Nonlinear Dynamics, Vol.53, Issue.4, pp.281-286, 2008.
  [15] V. Goodman, J.Sampfli, “The Mathematics of Finance: Modeling and Hedging”, The American Society, First Indian Edition, 2013.
  

  Citation
  M. P. Ghosh, R. M. Gor, "Solution of European Call Option by the First Integral Method," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.147-154, 2019

• Open Access   Article

  New Modification of Third-Order Iterative Method with Optimal Fourth-Order Convergence for Solving Nonlinear Equations

  Wartono, Rahmawati, R. Agustin

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.155-161, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.155161

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  Abstract
  Behl’s method is a third-order iterative method involving three functional evaluations for solving nonlinear equation. In this paper, we presented a new iterative method free second derivative with three real parameters by using second-order Taylor expansion. In order to avoid the second derivative, it is approximated by using equality of Chun-Kim’s method and Newton-Steffensen’s method. The result of study shows that the proposed method converges quartically and requires three evaluation of functions per iteration with efficiency index equal to 1.587401. Numerical simulation is presented to examine the performance of the proposed method by using several real test functions. The final results show that the proposed method is more efficient and perform better than some other kind of methods

  Key-Words / Index Term
  Behl’s method, Chun-Kim’s method, Third-order iterative method, Newton-Steffensen’s method, Numerical simulation

  References
  [1] A. C. Chapra, R. P. Canale, “Numerical Methods for Engineering with Programming and Software Application”, McGraw-Hill Publication, Singapore, pp. 194 – 209, 1998.
  [2] K. C. Gupta, V. Kanwar, S. Kumar, “A Family of Ellips Methods for Solving Non-Linear Equations”, International Journal of Mathematical Educations in Science and Technology, pp. 571 – 575. 2009.
  [3] S. Amat, S. Busquier, “On An Improvement of the Steffensen Method”, IMHOTEP, Vol. 4, No. 1, pp. 41 – 48, 2003.
  [4] S. Amat, S. Busquier, J. M. Gutierrez, “Geometric Construction of Iterative Functions to Solve Nonlinear Equations”, Journal of Computational and Applied Mathematics, Vol. 157, pp. 197-205, 2003.
  [5] S. Amat, S. Busquier, J. M. Gutierrez, M. A. Hernandez, “On Global Convergence of Chebyshev’s Iterative Method”, Vol. 230, pp. 17 – 21, 2008.
  [6] R. Behl, V. Kanwar, K. K. Sharma “Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equatiaons”. Journal of Applied Mathematics Vol. 2012, pp. 1- 22, 2012.
  [7] D. Jiang, D. Han,”Some One-Parameter Families of Third-Order Methods for Solving Nonlinear Equations”, Applied Mathematics and Computations, Vol. 195, pp. 392 – 396, 2008.
  [8] V. Kanwar, S. K. Tomar, “Exponentially Fitted Variants of Newton’s Method with Quadratic and Cubic Convergence”, International Journal of Computer Mathematics, Vol. 86, No. 9, pp. 1603 – 1611, 2009.
  [9] A. Melman, “Geometry and Convergence fo Euler’s and Halley’s Methods”, SIAM Review, Vol. 39, No. 4, pp. 726 – 735, 1997.
  [10] A. Rafiq, A. Javeria, “New Iterative Methods for Solving Nonlinear Equations by Using Modified Homotopy Pertubation Method”, Acta Unversitatis Apulensis, Vol. 18, pp. 129 – 137, 2009.
  [11] J. F. Traub, “Iterative Methods for the Solution of Equations”, Prentice-Hall, Inc, Englewood Cliffs, N.Y, pp. 1 – 36, 1964.
  [12] C. Chun, Y. Kim, “Several New Third-Order Iterative Methods for Solving Nonlinear Equations”. Acta Applied Mathematics, Vol. 109, pp. 1053 – 1063. 2010.
  [13] S. Abbasbandy, “Modified Homotopy Perturbation Method for Nonlinear Equations and Comparison with Adomian Decomposition Method”, Applied Mathematics and Computation. Vol. 172, pp. 431–438, 2006.
  [14] C. Chun, “Iterative Methods Improving Newton’s Method by the Decomposition Method”, Computer and Mathematics with Applications, Vol. 50, pp. 1559 – 1568, 2005.
  [15] C. Chun, “A One-Parameter Family of Third-Order Methods to solve nonlinear Equations”, Applied Mathematics and Computation. Vol. 189, pp. 126 – 130, 2007.
  [16] M. A. Noor, “Iterative Methods for Nonlinear Equations Using Homotopy Pertubation Technique”, Applied Mathematics & Information Sciences, Vol 4, No. 2, pp. 227 – 235, 2010.
  [17] S. Abbasbandy, “Improving Newton-Raphson Method for Solving Nonlinear Equation by Modified Adomian Decomposition Method,”Applied Mathematics and Computation. Vol. 145, pp. 887-893, 2003.
  [18] M. Frontini, E. Sormani, “Some Variant of Newton’s Method with Third-Order Convergence”, Applied Mathematics and Computation, Vol. 140, pp. 419 – 426, 2003.
  [19] A. Y. Ozban, “Some New Variants of Newton’s Method”, Applied Mathematics Letters, Vol. 17, pp. 677 – 682, 2004.
  [20] J. R. Sharma, “A Composite Third-Order Newton-Steffensen Method for Solving Nonlinear Equations”. Applied Mathematics and Computation, Vol. 169, pp. 242 - 246. 2005.
  [21] S. Weerakoon, T. G. I. Fernando, “A Variant of Newton’s Method with Accelerated Third-Order Convergence”, Applied Mathematics Letters, Vol. 13, pp. 87 – 93, 2000.
  [22] H. T. Kung, J. F. Traub, “Optimal Order of One-point and Multipoint Iteration”, Journal of the Association for Computing Machinery, Vol 21, No. 4, 643 – 651, 1974.
  [23] M. Kansal, V. Kanwar, S. Bhatia, “Optimized Mean Based Second Derivative-Free Families of Chebyshev-Halley Type Methods”, Numerical Analysis and Applications, Vol. 8, No.2, pp. 129 – 140, 2016.
  [24] Wartono, M. Soleh, I. Suryani, Muhafzan, “Chebysev-Halley’s Method without Second Derivative of Eight-Order Convergence”. Global Journal of Pure and Applied Mathematics. Vol. 12, No. 4, pp. 2987-2997, 2016.
  [25] Wartono, M. Soleh, I. Suryani, Zulakmal, Muhafzan, “A New Variant of Chebyshev-Halley’s Method without Second Derivative with Convergence of Optimal Order”. Asian Journal of Scientific Research, Vol. 11, No. 3, pp. 409 - 414, 2018.
  

  Citation
  Wartono, Rahmawati, R. Agustin, "New Modification of Third-Order Iterative Method with Optimal Fourth-Order Convergence for Solving Nonlinear Equations," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.155-161, 2019

• Open Access   Article

  Fixed Point Theorem for Semi-Compatible and R-Weakly Commuting in Intuitionistic Fuzzy Metric Space

  A. Muraliraj, S. Sumithiradevi

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.162-166, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.162166

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  Abstract
  In this paper, Fixed point theorem is proved by using four self maps .we split into pair, one in semi-compatible and another in R-weakly commuting mapping mainly using intutionistic fuzzy metric space. Our result extend and generalize and also illustrate some result.

  Key-Words / Index Term
  Fuzzy set, Fuzzy metric space , Intuitionisitc fuzzy metric space , semi-compatible, R-weakly commuting

  References
  [1]. Alaca,C.,Turkoglu,D and Yildiz,C (2006), “Fixed points in Intuitionistic Fuzzy metric spaces,”Chaos,Solitons and Fractals, Vol 29,No. 5,2006.pp.1073-1078.
  [2]. Alaca,C.,Turkoglu,D and Yildiz,C and Cho Y.J (2006) ‘Common fixed point theorems in intuitionistic fuzzy metric spaces,’Journal of Applied Mathematics and Computing, Vol.22,No.1-2,2006.pp.411-424.
  [3]. Alaca,I.Altun and D.Turkoglu,” On compatible mappings of type(I) and type(II) in intuitionistic fuzzy metric spaces,” communications of the Korean Mathematical society,Vol23,No.3,2008,pp.427-446.
  [4]. Atanassov,K.(1986) Intuitionistic Fuzzy sets, Fuzzy sets and system, Vol,20,pp.87-96.
  [5]. Y.J.Cho, B.K.Sharma and D.R.Sahu, Semi-compatiblity and fixed points,Math Japonica 42 (1995),91-98.
  [6]. A.George,P.veeramani on some results in fuzzy metric spaces fuzzy sets and systems 64(1994)395-399
  [7]. G..Jungck,” compatible mappings and common fixed point(2)” ,internat.J.Math.Math.Math.Sci.(1988),285-288.
  [8]. Kramosil.I and Michalek.J, Fuzzy metric and Statistical metric spaces, Kybernetika,11(1975),336-344.
  [9]. Schweizer,B and Sklar,A.(1920),” Statistical metric spaces,” Pacific Journal of Mathematics Vol.10,pp.313-334.
  [10]. B.Singh and S.Jain, “ Semi-compatiblility,Compatiblility and fixed point theorems in fuzzy metric space” Journal of the chungcheong mathematical society Vol.18,No,1.April 2005.
  [11]. .A.Zadeh, Fuzzy sets, Infor. and control, 8(1965)
  

  Citation
  A. Muraliraj, S. Sumithiradevi, "Fixed Point Theorem for Semi-Compatible and R-Weakly Commuting in Intuitionistic Fuzzy Metric Space," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.162-166, 2019

• Open Access   Article

  Relation between Lp-Riemann Derivative, Approximate Riemann Derivative and Riemann Derivative

  T. K. Garai

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.1 , pp.167-172, Feb-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.167172

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  Abstract
  As the Definition of Lp-derivative is such that which contains only the absolute value of the function and therefore it is not possible to define the Lp-derivates from the definition of Lp-derivative. So to remove this difficulty S.N. Mukhopadyay and S.Ray uses a special technique to define them in their paper [2]. In this article we define the Lp-Riemann Derivative using the same technique as it is used to define the Lp-derivates in [2] and relation between approximate Riemann Derivative and Riemann derivative are studied.

  Key-Words / Index Term
  Riemann derivative, Approximate Riemann derivative Lp-Riemann derivative Holder`s inequality

  References
  [1] S. N. Mukhopadhyay, Higher order derivatives, Chapman and Hall/CRC, Monographs and surveys in Pure and Applied Methematics, 144 (2012).
  [2] S.N.Mukhopadhyay and S.Ray, "Relation between Lp-derivates and Peano, approximate Peano and Borel derivates of higher order". Real Analysis Exchange, 41(1)(2015/2016) 1-22.
  [3] J.M.Ash, Generalisations of Riemman derivetive, Trans. American Math. Soc., 126 (1967), 181-199.
  

  Citation
  T. K. Garai, "Relation between Lp-Riemann Derivative, Approximate Riemann Derivative and Riemann Derivative," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.1, pp.167-172, 2019