Volume-9 , Issue-1 , Feb 2022, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Bipolar Double-Framed Uncertainty Ideal Structures

  G. Rethnarexlin, G. Subbiah, V. Nagarajan

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.1 , pp.1-6, Feb-2022

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  Ideal concepts are involved in many mathematical applications various author have been studied and analytical in different ways. In this paper, the concept of bipolar double-framed fuzzy subalgebra’s in terms of R-ideals is proposed. Also the relationship between bipolar double-framed fuzzy soft ideal and bipolar double-framed fuzzy soft R-ideals is studied some interesting results also analyzed.

  Key-Words / Index Term
  soft set, fuzzy set, bipolar fuzzy soft set, double-framed fuzzy set, R-ideal, subalgebra, soft algebra, approximate function, universe

  References
  [1] Abdullah. S, Aslam. M and Ullah. K, Bipolar fuzzy soft sets and its applications in decision making problem,JIntel. FuzzySyst. 27(2):729–742, 2014.
  [2] Ali. M.I, Feng. F, Liu. X, et.al, On some new operations in soft set theory, Comput Math Appl. 57:1547–1553, 2009.
  [3] Akram. M,Kavikumar. J and Khamis. A.B, Characterization of bipolar fuzzy soft–semigroup, Indian J. Sci. Technol. 7(8):1211–1221, 2014.
  [4] Cho. Y. U, Lee. K. J & Jun. Y. B, A study on double-framed soft near-rings, Applied Mathematical Sciences, 9(18), 867-873, 2015.
  [5] Farhat Nisar, Bipolar-valued Fuzzy K-subalgebras, World Applied Sciences Journal, 14(12), 1914-1919, 2011.
  [6] Hadipour. A. R, Double-framed Soft BF-algebras, Indian Journal of Science and Technology, 7(4), 491-496, 2014.
  [7] Hussain. R. J, Sampath. K & Jayaraman. P, Applications of Double-Framed Soft Ideal Structures over Gamma Near-Rings, Global Journal of Pure and Applied Mathematics, 13(9), 5101-5113, 2017.
  [8] Jun. Y.B, Soft BCK/BCI-algebras, Comput.Math.Appl.; 56:1408–1413, 2008.
  [9] Jun. Y.B and Park. C.H, Applications of soft sets in ideal theory of BCK/BCI-algebra, Inform Sci.; 178:2466–2475, 2008.
  [10] Jun. Y.B & Ahn. S.S (2012), Double-framed soft sets with applications in BCK/BCIalgebras, Journal of Applied Mathematics, 2012.
  [11] Khan. A, Izhar. M & Sezign. A, Characterizations of Abel Grassmann’s Groupoids by the Properties of Their Double-Framed Soft Ideals, International Journal of Analysis and Applications, 15(1), 62-74, 2017.
  [12] K.M.Lee, Bipolar valued-valued fuzzy sets and their operations, Proc.Int.Conf. on Intelligent Technologies, Bangkok, Thailand. 307-312, 2000.
  [13] Molodtsov.D.A, Soft set theory-firstresults, Comput. Math. Appl.;37:19–31, 1999.
  [14] Maji. P.K, Biswas. R and Roy. A.R, Soft set theory, Comput. Math. Appl.;45:555–562, 2003.
  [15] 15.Naz. M and Shabir.M, On bipolar fuzzy soft sets their algebraic structures and applications, J. Intel, FuzzySyst.;26(4):1645–1656, 2014.
  [16] Naz. M, Some studies on algebraic structure of soft sets,P.hd Dissertion Quaidi-Azam University Islamabad, Pakistan. 2015.
  [17] G.Rethnarexlin, G.Subbiah and V.Nagarajan, Double- framed G-invariant N-fuzzy soft G-modules, International journal of Mathematical trends and technology, Vol.65, No.7, 130 -138, 2019.
  [18] G.Rethnarexlin, G.Subbiah and V.Nagarajan, Double- framed created retrenchment N-fuzzy soft ideal structures, IJSRMSS, Vol.6, No.5, 34-39, 2019.
  [19] Shabir. M & Khan. S, Double framed soft topological space, Annals of Fuzzy Mathematics and Informations, x(x), 1-xx, 2016.
  [20] Khan. A, Izhar. M & Khalaf. M.M, Double-framed soft LAsemigroups, Journal of Intelligent & Fuzzy Systems, 33(6), 3339-3353, 2017.
  [21] Sezgin. A and Atagun. A.O, Soft groups and normalistic soft groups, Comput. Math. Appl.;62(2):685–689, 2011.
  [22] Zhang.W.R,Bipolarfuzzysets,1998IEEEInternationalConferenceonFuzzySystemsProceedings, IEEE World Congress on Computational Intelligence (Cat. No.98CH36228), Anchorage, AK, USA, pp.835-840 vol.1, 1998. doi:10.1109/fuzzy.1998.687599.
  [23] L. A. Zadeh, Fuzzy sets, Inform. Control, 8(3), 338–353, 1965.
  

  Citation
  G. Rethnarexlin, G. Subbiah, V. Nagarajan, "Bipolar Double-Framed Uncertainty Ideal Structures," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.1, pp.1-6, 2022

• Open Access   Article

  Accessible Formulas for Computing the Magnitude of Resultant Vector in 2 and 3-Dimensions

  O.E. Ikuemuya

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.1 , pp.7-13, Feb-2022

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  This paper presents accessible alternative formulas for solving geometry related problems associated with the use of Pythagoras theorem in calculating the magnitude of resultant vectors in geometry. The proposed formulas are simple and less cumbersome than the normal Pythagoras theorem when used in computing the magnitude of the resultant vector in 2 or 3-dimensions. The usage of the new formulas does not require finding the square roots of numbers which is most times very difficult to obtain without a calculator especially when the numbers involved are not perfect squares, hence its usage will drastically reduce the occurrence of irrational numbers namely square roots of non-perfect squares e.g in mathematics, since the square root of such non-perfect squares numbers usually occur when the Pythagoras theorem is applied in geometrical computations. The proposed formulas only make use of basic arithmetic operation such as addition, division and multiplication which can be done seamlessly with or without the use of calculators and it produces results that agree quite well with the results obtained using the usual Pythagoras? theorem. Also, in this paper, it was shown that the sum of the magnitude of the opposite side and adjacent side of a right-angle triangle or the sum of the magnitude of two vectors acting perpendicularly in 2-dimensions is reduced by an average constant factor of 0.7 to give the magnitude of the resultant vector or the length of the hypotenuse, and in 3-dimensions, the sum of the magnitude of the 3 vectors acting perpendicularly is been reduced by an average constant factor of 0.6 to give the magnitude of the resultant vector.

  Key-Words / Index Term
  Average constant factor, Pythagoras theorem, Magnitude of resultant factor, Ikuemuyas formula

  References
  [1] Clark Hardwood L. and Norton F.G.J., “Ordinary level mathematics with answers (8th Edition)” Heinemann Educational Books LTD, 1984.
  [2] Loomis, E.S., “The Pythagorean proposition: Its demonstration analyzed and classified bibliography of sources for data of the four kinds of proof, Washington DC” National council of teachers of mathematics, 1968.
  [3] Swaminathan S, The Pythagoras theorem. J Biodivers Biopros Dev 1:128. Doi:10.4172/2376-0214.1000128, 2014.
  [4] Ngoc-Loan Nguyen, David E Meltzer, Initial understanding of vector concepts among students in introductory physics courses. American journal of physics, 71 (6), pp.630-638, 2003.
  [5] U. Wutchana, N. Emarat, Finding resultant vectors using a rubber band. Iopscience, physics education 49 (2), 141, 2014.
  [6] CL Maknun, R Rosjanuardi, A Jupri, From ratios of right triangle to unit circle: An introduction to trigonometric functions Journal of physics: 1157 (2), 022124, 2019.
  [7] PEARSON mathematics 9 (2nd Ed.), ?Pythagoras theorem? Chap. 2, pp.81,115.
  [8] Godfrey & Siddons, Practical geometry based on the various geometry books Cambridge university press pp.39-40.
  

  Citation
  O.E. Ikuemuya, "Accessible Formulas for Computing the Magnitude of Resultant Vector in 2 and 3-Dimensions," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.1, pp.7-13, 2022

• Open Access   Article

  A Competitive Study on the Euler and Different Order Runge-Kutta Methods with Accuracy and Stability

  H. Rahman, A. Khair, N. Sultana

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.1 , pp.14-18, Feb-2022

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  Numerical methods in solving ordinary differential equations (ODEs) play an essential role in dealing with different mathematical, physical, and engineering problems. The accuracy and stability of the numerical methods are the critical factors for examining their performances in solving related problems. In this study, a comparison is made between some well-known methods, namely the Euler and different order Runge-Kutta (RK) methods, which are RK(2,2), RK(3,3), and RK(4,4) schemes, in terms of accuracy and stability. We have tested the numerical accuracy of the mentioned methods through the root mean square error (RMSE) value. Furthermore, the stability polynomials of the methods are determined, and their contour plot is made to analyze the methods’ stability. We have got the ordered relation “Euler RK(2,2) RK(3,3) RK(4,4)” both for the accuracy and stability tests. According to the ordered relation, it is clear that the RK(4,4) method is the most accurate and stable scheme among the test methods.

  Key-Words / Index Term
  Euler method, Different order Runge-Kutta methods, Accuracy, Stability, Root mean square error, Stability polynomial

  References
  [1] R.L. Burden, J.D. Faires, “Numerical Analysis,” Cengage Learning, USA, 2011.
  [2] D. Kumar, G.C. Paul, “Solitary and periodic wave solutions to the family of nonlinear conformable fractional Boussinesq-like equations,” Mathematical Methods in the Applied Sciences, Vol.44, Issue.4, pp. 3138-3158, 2021.
  [3] D. Kumar, A. Joarder, A. Hoque, G.C. Paul, “Investigation of dynamics of nematicons in liquid crystals by extended sinh-Gordon equation expansion method,” Optical and Quantum Electronics, Vol.51. No.7, pp.1-36, 2019.
  [4] G.C. Paul, A.H.M. Rashedunnabi, M.D. Haque, “Testing efficiency of the generalised (G`/G) G`/G -expansion method for solving nonlinear evolution equations,” PRAMANA-Journa of Physics, Vol.92, No.2, pp.1-14, 2019.
  [5] G.C. Paul, F. Bilkis, M.E. Ali, M.C. Barman, “Settling time of solid grains in gaseous giant protoplanets,” Planetary and Space Science, Vol.200, Issue.1, pp. 105212, 2021.
  [6] G.C.Paul, S. Khatun, M. Nuruzzaman, D Kumar, M.E. Ali, F. Bilkis, M.C. Barman, “Solving protoplanetary structure equations using Adomian decomposition method,” Heliyon, Vol.7, Issue.10, pp.e08213, 2021.
  [7] B.N. Kharrat, G.A. Toma, “Development of Homotopy Perturbation Method for Solving Nonlinear Algebraic Equations,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.2, pp.47-50, 2020
  [8] G.C. Paul, S. Senthilkumar, H. Rahman, “On the implementation of novel RKARMS (4,4) algorithm to study the structures of initial extrasolar giant protoplanets,” Heliyon, Vol.6, Issue.1, pp. e02865, 2020.
  [9] J.D. Lambert, “Numerical Methods for Ordinary Differential Systems: The Initial Value Problem,” John Wiley & Sons, USA, 1991.
  [10] S.C. Chapra, R.P. Canale, “Numerical Methods for Engineers,” McGraw-Hill New York, USA, 2015.

  Citation
  H. Rahman, A. Khair, N. Sultana, "A Competitive Study on the Euler and Different Order Runge-Kutta Methods with Accuracy and Stability," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.1, pp.14-18, 2022

• Open Access   Article

  Estimation Methods of Kumaraswamy Lindley Regression Model with Applications on Egyptian Stock Exchange Data

  S.A. Mohamed, S.M. Mohamed

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.1 , pp.19-23, Feb-2022

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  In this paper, we present the different methods for estimating the parameters of the Kumaraswamy Lindley Regression Model using different methods, which are, respectively, Maximum Likelihood Estimation, Ordinary least-squares estimators, The weighted least squares(WLSE), Cramer-Von-Mises estimation, Method of Anderson-Darling, These methods were compared using each of the following statistical measures An Akaike information criterion (AIC), Consistent Akaike information criterion(CAIC), Bayesian information criterion(BIC), The application was carried out on data from the Egyptian Stock Exchange, The paper concluded that the method of the Maximum Likelihood Estimation was lower in value than each of the previous measures, and thus it is the best in

  Key-Words / Index Term
  Kumaraswamy Lindley Regression, Maximum Likelihood Estimation(MLE). Ordinary least-squares estimators (OLS), weighted least squares(WLSE), Cramer-Von-Mises estimation (CVM), Method of Anderson-Darling

  References
  [1] 1-Afify, A. Z., and Mohamed, O. A.). "A new three-parameter exponential distribution with variable shapes for the hazard rate: estimation and applications. Mathematics", Vol 8, , Issue.3, pp.120-132, 2020.
  [2] 2- Ahmed Z. Afify and Haitham M. Yousof"The Exponentiated Weibull-Pareto Distribution with Application", Journal of Statistical Theory and Applications, Vol. 15, No. 4, pp 326-344,2016
  [3] -Dey, S., Nassar, M. and Kumar, D.". Alpha power transformed inverse Lindley distribution": a distribution with an upside-down bathtub-shaped hazard function." Journal of Computational and Applied Mathematics, vol 2 Issue 3,pp348, 130-145.2019
  [4] . Elgohari, H. and Yousof, H. M.). "New Extension of Weibull Distribution: Copula, Mathematical Properties, and Data Modeling. Statistics, Optimization & Information Computing", 8(4), 972-993. ,2020 https://doi.org/10.19139/soic-2310-5070-1036
  [5] Gupta, R. D., and Kundu, D. "Generalized exponential distribution: different methods of estimations". Journal of Statistical Computation and Simulation, vol69, pp315-337, 2001..
  [6] Gauthami P1 and Chacko V M"Dus Transformation of Inverse Weibull Distribution": An Upside-Down Failure Rate Model,), Volume 16, No 2,p 62,2021
  [7] Ibrahim, M., Altun, E. and Yousof, H. M. "New distribution for modeling lifetime data with different methods of estimation and censored regression modeling. Statistics, Optimization" Information Computing, vol8 Issue(2), pp610-630.,2021
  [8] Mansour, M. M., Butt, N. S., Ansari, S. I., Yousof, H. M., Ali, M. M., and Ibrahim, M. "A new exponentiated Weibull distribution`s extension: copula, mathematical properties, and applications. Contributions to Mathematics", 57–66. DOI: 10.47443/cm.2020.0018 pp.111-117, 2020..
  [9] Mazen Nassar. Ahmed Z. Afify_, Mohammed K. Shakhatreh"Estimation Methods of Alpha Power Exponential Distribution with Applications to Engineering and Medical Data", Pak.j.stat.oper.res. Vol.16 No.1 2020 pp 149-166
  [10] Mead, M. E., Cordeiro, G. M., Afify, A. Z. and Al Mofleh, H. "The alpha power transformation family: properties and applications". Pak. J. Stat. Oper. Res., vol 15,pp( 525-545),2019.
  [11] Kavya, P. and Manoharan, M). "On a Generalized lifetime model using DUS transformation." Joshua, V., Varadhan, S., Vishnevsky, V. (Eds). Applied Probability and Stochastic Processes.Infosys Science Foundation Series, Springer, Singapore, 281–291...
  [12] Gauthami, P. and Chacko, V. M. "DUS transformation of Inverse Weibull distribution: An upside-down failure rate model, Reliability: Theory and Applications", Vol 16, No 2(62),pp58-71,2021
  [13] Salah, M. M., El-Morshedy, M., Eliza, M. S. and Yousof, H. M. "Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications, and Validation Testing. Mathematics," vol 8, N(11), PP1949.
  [14] Shakhatreh, M. K., Lemonte, A. J. and Cordeiro, G. M. 2019. On the generalized extended
  [15] exponential-Weibull distribution: properties and different methods of estimation. International Journal of Computer Mathematics. DOI:10.1080/00207160.2019.1605062.

  Citation
  S.A. Mohamed, S.M. Mohamed, "Estimation Methods of Kumaraswamy Lindley Regression Model with Applications on Egyptian Stock Exchange Data," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.1, pp.19-23, 2022

• Open Access   Article

  Some Common Fixed Point Theorems in Complex Valued Intuitionistic Fuzzy Metric Spaces

  M. Jeyaraman, V.B. Shakila

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.1 , pp.24-31, Feb-2022

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  In this paper, we aim to prove some common fixed point theorems for contraction condition and pairs of occasionally weakly compatible mappings satisfying some conditions in complex valued intuitionistic fuzzy metric spaces.

  Key-Words / Index Term
  Common fixed point, Occasionally weakly compatible mappings, Complex valued, Continuous t-norm, Intuitionistic fuzzy set

  References
  [1] K. Atanassov, “ Intuitionistic Fuzzy Sets,” Fuzzy sets and systems, 20, pp. 87 – 96, 1986.
  [2] A. Azam, B. Fisher and M. Khan, “Common fixed point theorems in complex valued metric space,” Numerical Functional Analysis and Optimization 32, pp. 243 – 253, 2011.
  [3] J. J. Buckley, “Fuzzy complex numbers,” Fuzzy Sets and Systems, 33,pp. 333 – 345, 1989.
  [4] A. George and P. Veeramani, “On some results in fuzzy metric spaces,” Fuzzy sets and systems, 64, pp. 395 – 399, 1994.
  [5] G. Jungck, “Compatible mappings and common fixed points,” Internat. Math. J. Maths. Sci., 9, pp. 771 – 779, 1986.
  [6] I. Kramosil and J. Michalek, “Fuzzy metric and statistical spaces,” Kybernetica, 11, pp. 336 – 344, 1975.
  [7] J. H. Park, “Intuitionstic fuzzy metric spaces,” Chaos, Solitons Fractals, 22, pp.1039 – 1046, 2004.
  [8] D. Ramot, R. Milo, M. Friedman, and A. Kandel, “Complex fuzzy sets,” IEEE Transactions of Fuzzy System, 10, 2002.
  [9] R. Saadati, J. H. Park, “On the intuitionstic fuzzy topological spaces,” Chaos Solitons Fractals, 27, pp. 331 – 344.
  [10] D. Singh, V. Joshi, M. Imdad, P. Kumar, “A novel framework of complex valued fuzzy metric spaces fixed point theorems,” Journal of Intelligent and Fuzzy systems, 30(6), pp. 3227 – 3238, 2016.
  [11] Uday Dolas, “A common fixed point theorem in fuzzy metric spaces using common E.A. Like property,” Journal of Applied Mathematics and computation, 2(6), pp. 245 – 250, 2018.
  [12] L. A. Zadeh, “Fuzzy sets,” Inform. and Control, 8, pp. 338 – 353, 1965.

  Citation
  M. Jeyaraman, V.B. Shakila, "Some Common Fixed Point Theorems in Complex Valued Intuitionistic Fuzzy Metric Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.1, pp.24-31, 2022

• Open Access   Article

  Enhanced Estimation of Population Mean in Presence of Errors on a Survey Variable in Stratified Two-Phase Sampling

  R. Onyango, B. Oduor, F. Odundo

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.1 , pp.32-39, Feb-2022

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  The present study proposes a new mean estimator using stratified two-phase sampling in the presence of non-response and measurement errors on a survey variable. The proposed estimator is based on auxiliary attribute and variable information. Up to the first degree of approximation, expressions for the bias and mean squared error of the proposed estimators are derived. Members of the family of the proposed generalized class of estimators are identified and studied. The performance of the proposed estimator is theoretically compared to that of existing mean estimators. A numerical study is conducted using a real-world data set to compare the efficiencies of the proposed estimators with other existing mean estimators. The proposed estimators outperform other existing mean estimators in the absence and presence of measurement errors, according to the numerical study. Furthermore, in the absence and presence of measurement errors, the values of the proposed estimators` percent relative efficiencies decrease as the inverse sampling rate and non-response rate increase.

  Key-Words / Index Term
  Bias, Mean squared error, Efficiency, Non-response and Measurement errors

  References
  [1] J. Shabbir, A. Sagir, “Estimation of Finite Population Mean in Stratified Random Sampling Using Auxiliary Attribute(s) under Non-Response,” Pakistan Journal of statistics and operation research, Vol.8, Issue.1, pp.73-82, 2012. DOI: https://doi.org/10.18187/pjsor.v8i1.336
  [2] K. Kumar, A. Kumar, “Estimation of Population Mean Using Auxiliary Attribute in the Presence of Non-Response,” International Journal of Computational and Theoretical Statistics, Vol.6, Issue.1,2019.DOI:http://dx.doi.org/10.12785/ijcts/060106
  [3] S. Riaz, M. A. Darda, “Some Classes of Estimators in the Presence of Non-Response Using Auxiliary Attribute,” Riaz and Darda. Springer Plus, Vol.5, Issue.1, 2016. DOI: 10.1186/s40064-016-2922-x
  [4] S. Bhushan, P. K Misra, S. Yadav, “An Unbiased Estimator for Population Mean Using an Attribute and an Auxiliary Variable,” Advances in Dynamical Systems and Applications, Vol.12, Issue.1, pp. 29-39, 2017.
  [5] S. Bhushan, R. Gupta, “Class of Log-Type Estimators for Population Mean Using Auxiliary Information on an Attribute and a Variable Using Double Sampling Technique,”. International Journal of Computational and Applied Mathematics, Vol. 14, Issue. 1, pp. 1-12, 2019.
  [6] S. Mir, S. Maqbool, T. A Raja, S. A. Mir, M. I Jeelani, M. A. Bhat , “Improved Family of Ratio Type Estimators for Estimating Population Mean using Conventional and Non-Conventional Location Parameters,” Revista investigacion operacional, Vol.38, Issue.5, pp. 499-513, 2017.
  [7] M. Javed, M. Irfan, S. H. Bhatti, R. Onyango, “A Simulation-Based Study for Progressive Estimation of Population Mean Through Traditional and Non-Traditional Measures in Stratified Random Sampling” Journal of Mathematics, 2021. Article ID 9038126. https://doi.org/10.1155/2021/9038126.
  [8] K. I. Rather, R. Yousuf, “Improved Estimator for Estimating the Population Mean In Simple Random Sampling,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.5, pp.16-18, 2020. DOI: https://doi.org/10.26438/ijsrmss/v7i5.1618
  [9] M. K. Chaudhary, A. Kumar, “Use of Double Sampling Scheme in Estimating the Mean of Stratified Population Under Non-Response,” Statistica, Vol. LXXV, Issue. 4, 2015.
  [10] A. E. Anieting, E. I. Enang, “Two-Phase Stratified Sampling Estimator For Population Mean in the Presence of Nonresponse Using One Auxiliary Variable,” Mathematical Journal of Interdisciplinary Sciences, Vol. 8 issue., 2, pp. 49-56, 2020.
  [11] G. K. Vishwakarma, S. Neha, A Kumar, “Computing the Combined Effect of Measurement Errors and Non-Response Using Factor Chain-Type Class of Estimator,” The Philippine Statistician, Vol. 68, Issue. 1, pp. 27-39, 2019.
  [12] K. D Yadav, M. Devi, S. K. Yadav, “Estimation of Finite Population Mean Using Known Coefficient of Variation in the Simultaneous Presence of Non-Response and Measurement Errors Using Double Sampling Scheme.” Journal of Reliability and Statistical Studies, Vol.11, Issue. 1, 51-66, 2018.
  [13] P. Singh, R. Singh, N. C Bouza “Effect of Measurement Error and Non-Response on Estimation of Population Mean,” Revista Investigacion Operacional, Vol. 39, Issue. 1, pp. 108-120, 2018.
  [14] C. N. Bouza, R. Singh, M. Mishra, “Estimation in Stratified Random Sampling in the Presence of Errors,” Revista Investigacion Operacional, Vol. 41, Issue. 1, pp. 123-135, 2020.
  [15] E. Zahid, J. Shabbir, “Estimation of Population Mean in the Presence of Measurement Error and Non-response Under Stratified Random Sampling. PLos ONE, Vol. 13, Issue. 2, 2018: e0191572. DOI: https://doi.org/10.1371/journal.pone.0191572.
  [16] Z. Ahmad, M. Iqra, M. Hanif, “Regression Estimator in Two-Phase Sampling Using Multi-auxiliary Information in the Presence of Non-Response and Measurement Error at Second Phase” Journal of Applied Probability and Statistics, Vol. 9, Issue. 2, pp. 41-53, 2014.
  [17] S. Bhushan, A. Kumar, “On Some Estimators of Population Mean Under Double Sampling with Measurement Error and Non-Response,” International Journal of Computation and Applied Mathematics, Vol. 12, Issue. 1, pp. 141-165, 2017.
  [18] S. Kumar, S. Bhougal, N. S. Nataraja, “Estimation of Population Mean in the Presence of Non-Response and Measurement Error,” Revista Colombiana de Estadistica, Vol. 38, Issue. 1, pp. 145-161, 2015.
  [19] M. K. Chaudhary, G. K. Vishwakarma, “A General Family of Factor-Type Estimators of Population Mean in the Presence of Non-Response and Measurement Errors,” International Journal of Mathematics and Statistics, Vol. 20, Issue. 1, pp. 83-93, 2019.
  [20] M. Azeem, M. Hanif, “Joint Influence of Measurement Error and Non-response on Estimation of Population Mean,” Communication in Statistics-Theory and Methods, Vol. 46, issue 4, pp. 1679-1693, 2018. DOI: https://doi.org/10.1080/03610926.2015.1026992.
  [21] J. W. Tukey, “Exploratory Data Analysis,” Addison-Welsey publishing Co., Reading, MA. 1976.
  [22] J. Hodges, E. Lehmann, “Estimation of Location Based on Ranks,” Annals of Mathematical Statistics, Vol. 34, Issue. 2, pp. 598-611, 1963.
  [23] M. H. Hansen, W. N. Hurwitz, “The Problem of Non-Response in Sample Surveys.” Journal of the American Statistical Association, Vol. 41, Issue. 236, pp. 517-529, 1946.
  [24] T. Zaman, C. Kadilar, “Exponential Ratio and Product Type Estimators of the Mean in Stratified Two-Phase Sampling.” AIMS Mathematics, Vol. 6, Issue. 6, 2021. DOI: 10:3934/ math.2021252

  Citation
  R. Onyango, B. Oduor, F. Odundo, "Enhanced Estimation of Population Mean in Presence of Errors on a Survey Variable in Stratified Two-Phase Sampling," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.1, pp.32-39, 2022

• Open Access   Article

  On Some Fourier Analogues of Dual Integrals Involving Bessel Functions and Trigonometrical Kernels

  Omprakash Atale

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.1 , pp.40-42, Feb-2022

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  The aim of our present work is to establish some Fourier type integrals that involve Bessel function and trigonometrical kernels using the Fourier inversion formula that was communicated by S. Ramanujan in his Quarterly Reports. Some possible applications to dual integral equations along with concluding remarks and further directions are presented.

  Key-Words / Index Term
  Ramanujan’s Fourier inversion theorem, Dual integrals

  References
  [1] I. Sneddon. “Dual integral equations with trigonometrical kernels”. Proceedings of the Glasgow Mathematical Association, Vol. 5, Issue 3, pp. 147-152. 1962.
  [2] K. Srivastava. “Dual Integral Equations with Bessel Function and Trigonometrical Kernels”. Proceedings of the Edinburgh Mathematical Society, Vol. 13, Issue 4, pp. 351-354, 1963.
  [3] W. Magnus and F. Oberhettinger, “Special functions of mathematical physics”, New York, p. 8, 1949.
  [4] B. Berndt, “Ramanujan’s Notebooks Part I”, Springer-Verlag, New York, 1985
  [5] G. N. Watson, “The theory of Bessel functions”, Cambridge, 1944.
  [6] J. Owndes. “Dual Integral Equations with Trigonometric Kernels. Proceedings of the Edinburgh Mathematical Society,Vol. 15, Issue 1, pp. 73-74, 1966.

  Citation
  Omprakash Atale, "On Some Fourier Analogues of Dual Integrals Involving Bessel Functions and Trigonometrical Kernels," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.1, pp.40-42, 2022

• Open Access   Article

  On some properties of Gauss Multiplication Theorem for k-gamma function

  Omprakash Atale

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.1 , pp.43-45, Feb-2022

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  In this paper, we have established some properties of the k-gamma function that arises from Gauss Multiplication Theorem. Furthermore, some related partial fractional decompositions are given which rescembles with the results of Ramanujan for ordinary gamma function.

  Key-Words / Index Term
  Gamma function, k-gamma function, Gauss mutiplcation theorem

  References
  Diaz, R. and Pariguan, E. On hypergeometric functions and Pochhammer k-symbol. Divulgaciones Mathematicas, Vol. 15, Issue 2, pp. 179-192, (2007).
  C.G. Kokologiannaki, Properties and inequalities of generalized k-gamma, beta and zeta functions, International Journal of Contemp. Math Sciences Vol 5, Issue 14, pp. 653-660, (2010).
  Mubeen Shahid, Rehman Abdur. A Note on k-Gamma Function and Pochhammer k-Symbol. Journal of Informatics and Mathematical Sciences, Vol 6, Issue 2, pp. 93-107, (2014).
  H. Alzer, On some inequalities for the gamma and psi function, Math. Comp. Vol 66, pp. 373–389, (1997).
  Kokologiannaki, Chrysi and Krasniqi, Valmir. Some properties of the k-Gamma function. Le Matematiche. Vol. 68, Issue 1, pp. 13-22, (2013)
  R. Diaz - C. Teruel, q, k-Generalized Gamma and Beta functions, J. Non-linear Math. Phys. Vol 12, Issue 1, pp. 118-134, (2005).
  V. Krasniqi, Inequalities and monotonicity for the ration of k-gamma function, Scientia Magna Vol. 6, Issue 1, pp. 40-45, (2010).
  M. Mansour, Determining the k-Generalized Gamma function ?k(x) by functional equations, Int. J. Contemp. Math. Sciences Vol. 4, Issue. 21, pp. 653-660, (2009).
  R. Diaz and C. Teruel, q k, -Generalized gamma and beta functions, J. Nonlinear Math. Phys., Vol. 12, pp. 118-134, (2005).
  Berndt, B. C. Ramanujan’s Notebooks. Springer, New York, NY (1985). Chp. 8.

  Citation
  Omprakash Atale, "On some properties of Gauss Multiplication Theorem for k-gamma function," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.1, pp.43-45, 2022