Volume-5 , Issue-4 , Aug 2018, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  A Modified Dual to Ratio Cum Product Estimator Using Two Auxiliary Variables in Stratified Sampling for Estimating Population Mean

  Asra Nazir, Rafia Jan, Showkat Maqbool and T.R. Jan

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.264-271, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.264271

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  Abstract
  The estimator proposed in literature by Tailor (2012) and the work on dual to the existing estimator has been extended by introducing additional parameters for estimating the population mean. The expression for the Mean Square Error (MSE) is obtained and compared with the existing. Numerical illustration is used to verify the PRE’S of the estimators.

  Key-Words / Index Term
  Auxiliary variable, Bias(B.),Mean Square Error(MSE), Stratified Sampling

  References
  [1]M.H.Hansen,W.N.Hurwitz,.and,M.Gurney “Problems and methods of the sample survey of business”.J.Am.Stat.Assoc,Vol.4,Issue.1,pp.173–189, 1946.
  [2],M.P.Singh”Ratio-cum-product method of estimation”,Metrika,Vol.12,Issue.1,pp.34–43, 1967.
  [3]C, Kadilar and,H. Cingi “Ratio estimators in stratified random sampling” .Biom.J.Vol.45,Issue2,pp.218–225,2003.
  [4]R.Tailor,S,Chouhan., and N. Garg,”A ratio-cum product estimator of population mean in stratified random sampling using two auxiliary variables”.StatisticaVol.22,Issue.3,pp.287-297,2012.
  [5] R. Tailor and H.A. Lone“Separate ratio cum product estimators of population mean using auxiliaryinformation”..J.Rajasthan.Stat.Asso,Vol.1,Issue.2,pp.94-102, 2012.
  [6] R. Tailor, and,S. Chouhan “Ratio cum product type exponential estimator of finite population mean in stratified random sampling”.Commun.Stat.TheoryMethods Vol.4,Issue.3,pp.343–354,2014.
  [7] R. Tailor, and H.A. Lone “Separate ratio type estimators of population mean in stratified random sampling”.J.ModernAppl.Stat.Methods Vol.13,Issue.1,pp.223–233, 2014.
  [8] N. Koyuncu and C. Kadilar “Family of estimators of population mean using two auxiliary variable in stratified sampling”.Commun.Stat.Theory.Methods .Vol.139,Issue.8,pp.2552-2558, 2009.
  [9] P.C. Etebong” An improved ratio estimator of finite population mean in stratified sampling”. European journal of statistics and probability .Vol .4,Issue.4,pp.12-17,2016.
  [10] P.C. Etebong, “Improved family of ratio estimator of finite population variance in stratified sampling”2018..DOI:10.19080/BBOAJ.2018.04.555659.
  [11]National Horticulture Board 2010. http://nhb.gov.in/statistics/area-productionstatistics.html
  

  Citation
  Asra Nazir, Rafia Jan, Showkat Maqbool and T.R. Jan, "A Modified Dual to Ratio Cum Product Estimator Using Two Auxiliary Variables in Stratified Sampling for Estimating Population Mean," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.264-271, 2018

• Open Access   Article

  Fixed point Theorems of Multivalued Mappings in Cone Metric Spaces via Cone C-Class function

  R. Krishnakumar, K. Dinesh, Arslan Hojat Ansari

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.272-277, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.272277

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  Abstract
  Let P be a subset of a Banach space E and P is normal and regular cone on E, we prove the existence of the fixed point for multi valued maps and φ–ψ- contractive mappings in cone metric spaces via cone C class functions.

  Key-Words / Index Term
  Cone metric space, Multivalued mappings, Fixed point, Cone C class function

  References
  [1]. R. Krishnakumar, M. Marudai “ Fixed Point Theorems of Multivalued Mappings in Cone Metric Spaces” Int. J. Contemp. Math. Sciences, Vol. 5, 2010, no. 31, 1533 - 1540
  [2]. Huang Gaung,Zhang Xian,”Cone metric spaces and fixed point theorems of contractive mappings” J.math.Anal. Appl.332(2007)1468-1476.
  [3]. H.Mohebi,Topical functions and their properties in a class of ordered Banach spaces,in continuous Optimization,Current Trends and Modern Applications, PartII, Springer, 2005.pp.343-361.
  [4]. H.Mohebi,H.Sadeghi,A.M.Rubinov,Best approximation in a class of normed spaces with star-shaped cone, Numer. Funct.Anal.Optim.27(3-4)(2006)411- 436.
  [5]. Sh.Rezapour,R.Hamlbarani,”Some notes on the Paper-Cone metric Spaces and fixed point theorems of contractive mappings,”-J.Math.Anal.Appl.345 (2008)719-724.
  [6] Seong Hoon Cho,Mi Sun Kim,”Fixed point theorems for general contractive multivalued mappings,”-J.Appl.Math.Informatics Vol.27 (2009)343- 350.
  [7] R.Krishnakumar, K. Dinesh, Fixed point of cyclic contraction functions in banach spaces, International Journal Of Innovative Research In Science ,Engineering And Technology, Vol. 5, Issue 7, July 2016, Pg-13316 -13319
  [8] A. H. Ansari, “Note on ϕ − ψ-contractive type mappings and related fixed point,”The 2nd Regional Conference on MathematicsAndApplications, PNU, September(2014), 377–380.
  [9] Arslan Hojat Ansari, Sumit Chandok, Nawab Hussin and Ljiljana Paunovic, “Fixedpoints of (ψ, φ)-weak contractions in regular cone metric spaces via new function”, J. Adv. Math. Stud. Vol. 9(2016), No. 1, 72–82.
  [10] R.Krishnakumar, K. Dinesh, “Existence of fixed points of fuzzy functions in complete metric spaces”, Proceedings of the International conference on applied mathematical models (Pg:240-242), ICAMM 2014 PSG College of Technology, Coimbatore, India
  [11] R.Krishnakumar, K. Dinesh, “Fixed Point Theorems of Fuzzy Function in Complete Metric Spaces” , International Journal Of Innovative Research In Science, Engineering And Technology, Vol. 6, Issue 7, July 2017, Pg-13557-13562
  [12] R. Krishnakumar, K. Dinesh, “Fuzzy Mapping and their Fixed Point Theorems in Complete Metric Spaces”International Journal of Scientific Research in Science, Engineering and Technology , Volume 3 , Issue 8, November-December-2017 , Pg: 241-249
  [13] Arslan Hojat Ansari, R. Krishnakumar, K. Dinesh,_ and D. Dhamodharan, “Fixed Point of Cyclic Contraction Mappings in Banach Spaces Via C-Class Function” Int. J. Math. And Appl., 6(1-E)(2018), 1085-1092
  [14] R. Krishnakumar, K. Dinesh, D. Dhamodharan, “Some Fixed Point Theorems in φ - ψ weak contraction on Fuzzy Metric Space” Int. J. Sci. Res. in Mathematical and Statistical Sciences Vol. 5(3), Jun 2018
  

  Citation
  R. Krishnakumar, K. Dinesh, Arslan Hojat Ansari, "Fixed point Theorems of Multivalued Mappings in Cone Metric Spaces via Cone C-Class function," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.272-277, 2018

• Open Access   Article

  Numerical Solution of two-dimensional time-dependent Schro ̈dinger equations using Haar wavelet

  Inderdeep Singh, Sheo Kumar

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.278-282, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.278282

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  Abstract
  An algorithm based on collocation points and two-dimensional Haar wavelet basis functions is developed for numerical solutions of two-dimensional time-dependent Schro ̈dinger equations. Error analysis of a proposed algorithm confirm the convergence of the present method. Numerical examples are performed to illustrate the accuracy of the proposed method.

  Key-Words / Index Term
  Haar wavelet method; 2D time-dependent Schro ̈dinger equations; Operational matrices; Error analysis

  References
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  [7] G. Hariharan, K. Kannan and R.K. Sharma, “Haar wavelet method for solving Fisher’s equation”, Applied Mathematics and Computational Science, Vol. 211, pp. 284-292, 2009.
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  [11] U. Lepik, “Solving diferential and integral equations by the Haar wavelet method”, revisted, International Journal of Mathematics and Computation, Vol. 1, Issue 8, pp. 43-52, 2008.
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  [13] I. Singh, S. Kumar, “Haar wavelet and Adomain decomposition method for solving third order partial differential equations arising in impulsive motion of a flat plate”, International Journal of Mathematical Modeling and Computation, Vol. 6, Issue 2, pp. 175-188, 2016.
  [14] I. Singh , S. Kumar, “Wavelet methods for solving three-dimensional partial differential equations”, Mathematical Sciences, Vol. 11, Issue 2, pp. 145-154, 2017.
  [15] Siraj-ul-Islam, I. Aziz, A.S. Al-Fhaid and A. Shah, “A numerical assessment of parabolic partial differential equations using Haar and Legendre wavelets”, Applied Mathematical Modelling, Vol. 37, pp. 9455-9481, 2013.
  [16] F.D. Tappert, “The parabolic approximation method”, in: J.B. Keller, J.S. Papadakis (Eds.), “Wave propagation and underwater acoustics”, in: Lecture Notes in Physics, Springer, Berlin, Vol. 70,pp. 224-287, 1977.
  [17] A. Kaushik, A. Kumar, “Numerical study of steady one dimensional Incompressible flow through a nozzle using simple algorithm”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 3, Issue 5, 1-7, 2016.
  [18] A. Kaushik, “ Numerical study of a steady state two dimensional Heat equation using TDMA technique”,International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 4, Issue 1, 6-11, 2017.
  

  Citation
  Inderdeep Singh, Sheo Kumar, "Numerical Solution of two-dimensional time-dependent Schro ̈dinger equations using Haar wavelet," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.278-282, 2018

• Open Access   Article

  On Contra Delta Generalized Pre-Continuous Functions

  J.B. Toranagatti

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.283-288, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.283288

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  Abstract
  In this paper, the notion of contra δgp-continuous functions is introduced by utilizing δgp-closed sets in topological spaces. Some of their fundamental properties are studied and the relationships of contra δgp-continuous functions with other related functions are discussed.

  Key-Words / Index Term
  δgp-open set, contra continuoud function, contra pre-continuous function, contra δgp-continuous function.

  References
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  δ-closure,θ-closure and generalized closed sets, Applied General Topology,Vol.6, pp.79-86,2005.
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  Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica,Vol.42, pp.27-34.1999.
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  Citation
  J.B. Toranagatti , "On Contra Delta Generalized Pre-Continuous Functions," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.283-288, 2018

• Open Access   Article

  Some Fixed Point Theorems on Generalized Contractive mappings in cone metric space

  R. Krishnakumar, R. Livingston

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.289-293, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.289293

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  Abstract
  The purpose of this paper is to obtain sufficient conditions for the existence of unique fixed point of generalized contractive type mappings on complete metric spaces.

  Key-Words / Index Term
  fixed point, generalized contractive mapping, complete cone metric space, sequently convergent.

  References
  [1] A. Beiranvand, S. Moradi, M. Omid and H. Pazandeh, Two fixed point theorem for special mapping, arXiv:0903.1504v1
  [math FA].
  [2] R. Krishnakumar , K. Dinesh , D. Dhamodharan, Some fixed point theoremsφ- ψ weak contraction on Fuzzy Metric
  spaces, International Journal of Scientific Research in Mathematical and Statistical Sciences, Volume-5, Issue-3, pp.146-
  152, June (2018)
  [3] R. Kannan, Some results on fixed points, Bull. Calc. Math. Soc.60, (1968), 71 – 76.
  [4] R. Krishnakumar, R. Livingston, “Study On Fixed Point Theorems in Complete Cone Metric Spaces” International
  Journal of Innovative Research in Science, Engineering and Technology,Volume 6, Issue 7, July 2017, 13526 – 13531.
  [5] H. Long – Guang and Z. Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl.,
  332, (2007), 1468 – 1476.
  [6] K. P. R. Sastry, Ch. Srinivasarao, K. Sujatha, G. Praveena, Cone metric spaces and fixed point theorems of Generalized
  Contractive mappings, International Journal of Computational Science and mathematics, Volume 3, Number 2 (2011), Pp.
  133 – 139.
  [7] S. Moradi, Kannan fixed point theorem on complete metric spaces and on generalized metric spaces depend on another
  function, arXiv: 0903. 1577v [Math. FA].
  [8] Sh. Rezapour and R. Hamlbarani, some notes on the paper “cone metric spaces and fixed point theorems of contractive
  mappings”, J. Math. Anal. Appl., 345, (2), (2008), 719 – 724.
  [9] Jose R. Morles and Edixon Rojas, Cone metric spaces and fixed point theorems of generalized contractive mappings Int.
  Journal of Math. Analysis, Vol. 4, 2010, no. 4, 175 – 184.
  

  Citation
  R. Krishnakumar, R. Livingston, "Some Fixed Point Theorems on Generalized Contractive mappings in cone metric space," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.289-293, 2018

• Open Access   Article

  Endorsement of Optimal ordering cycle implementing Quick Switching System with Single Sampling Plan with Permissible delay in Payments involving non-destructive testing

  Aruna H M, K.Pradeepa Veerakumari, S.Suganya

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.294-298, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.294298

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  Abstract
  Quick Switching System-1 intensifies the likelihood of identifying the defects at the same time curtails the sample size. It consists of two intensity of inspection namely, normal and tightened inspection based on the number of defects. Tightened inspection with less acceptance number is employed when there is a possibility of high number of defects otherwise normal inspection is applied. Economic ordering quantity with permissible delay in payment enables the consumer optimal ordering size with the least possible cost and permissible late payment. Application of QSS-1 in EOQ model in permissible delay in payment has the benefits of cost-effective, reliable quality products. Case study on casting defects is given. Numerical illustrations are also provided to validate the results.

  Key-Words / Index Term
  Quick Switching System-1; Normal inspection; Tightened inspection; Economic Ordering Quantity; Permissible delay in payments

  References
  [1]. Romboski L D. “An Investigation of Quick Switching Acceptance Sampling Systems” .Ph.D Thesis. Rutgers-The State University New Brunswick. New Jersey, 1969.
  [2].Schilling .E.G. “Acceptance Sampling in Quality Control”. Marcel Dekker, New York, 1982.
  [3]. Tsao.Y.C. “Optimal Ordering policy under Acceptance Sampling plan and trade credit financing”, Transaction E: Industrial Engineering. 17(2) :120-128, 2010.
  [4]. PradeepaVeerakumari.K, Aruna.H.M. “Application of SSP for determination of influence over trade credit with payment choice”, International Journal of pure and Applied Mathematics, 117(13),193-201, 2017.
  [5].PradeepaVeerakumari.K, Aruna.H.M., ”Determination of Economic Ordering Policies under Trade credit with Application of Zero Acceptance number Single Sampling by Attributes involving Destructive Testing, Inspection Errors”, International Journal of Scientific Research in Mathematical and Statistical Sciences,5(3),79-84, 2018.
  

  Citation
  Aruna H M, K.Pradeepa Veerakumari, S.Suganya, "Endorsement of Optimal ordering cycle implementing Quick Switching System with Single Sampling Plan with Permissible delay in Payments involving non-destructive testing," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.294-298, 2018

• Open Access   Article

  Epidemic Model with Vital Dynamics and a Saturated Incidence rate

  S.K. Tiwari, V.K. Gupta, Lakhan Nagar, Pradeep Porwal

  Review Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.299-305, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.299305

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  Abstract
  In this paper, we proposes a new SEIRS model with vital dynamics and a saturated incidence rate. We find equilibrium point, basic reproduction number and stability of the system.

  Key-Words / Index Term
  Epidemic Model, Saturated Incidence rate, Basic Reproduction number, Stability.

  References
  [1] P. Van den Driessche , J. Watmough ,” Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission”, Mathematical biosciences, 180, 29-48,2002,
  [2] J. Zhan , J. Li ,Z. Ma, “Global dynamics of an SEIR epidemic model with immigration of different compartment”, Acta Mathematica Scientia, 26, 551-567,2006.
  [3] N.Yi , Q. Zhang ,K. Mao,D. Yang ,Q. Li , “analysis and control of an SEIR epidemic system with nonlinear transmission rate” Mathematical and computer modeling, 50, 1498-1513, 2009.
  [4] C.Sun , Y. Hsieh ,”Global analysis of an SEIR model with varying population size and vaccination”, Applied Mathematical Modeling, 2685-2697, .2010
  [5] X. Zhou , J. Cui , “Analysis of stability and bifurcation for an SEIR epidemic model with saturated recovery rate” Communications in nonlinear Science and Numerical Simulatio,16.4438-4450, 2011.
  [6] H. Shu , D. Fan ,J. Wei, “Global stability of multi group SEIR epidemic models with distributed delays and Non linear transmission”, Non linear analysis: RealWord Applications, 13,1581-1592,2012.
  [7] Wang Xinli, “An SIRS epidemic model with Vital Dynamics and a Ratio Dependent Saturation incidence rate”, Discrete Dynamics in nature and society,1-9, 2015.
  [8] B. Trawicki , “Deterministic SEIRS epidemic model for modeling Vital Dynamics”, Vaccinations, and Temporary immunity.Mathematics,1-19, 2017.
  

  Citation
  S.K. Tiwari, V.K. Gupta, Lakhan Nagar, Pradeep Porwal, "Epidemic Model with Vital Dynamics and a Saturated Incidence rate," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.299-305, 2018

• Open Access   Article

  Anti-magic labeling for Boolean graph of path BG(P_n), (n≥4)

  T. Subhramaniyan and S. Suruthi

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.306-310, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.306310

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  Abstract
  A graph G is anti-magic if there is a labelling of G is a one-to-one mapping taking the edges onto 1, 2, ...., |E| such that the sum of the labels assigned to edges incident to distinct vertices are different. A conjecture of Hartsfield and Ringel states that every connected graph different from K_2 is anti-magic. Our main result validates this conjecture for Boolean graph of path P_(n) (n≥4).

  Key-Words / Index Term
  Boolean graph BG(G) Anti-magic Labeling

  References
  [1] N. Alon, G. Kaplan, A. Lev, Y. Roditty, R. Yuster, Dense graphs are antimagic, Journal of Graph Theory 47 (2004) 297–309.
  [2] W. Brown, Antimagiclabelings and the antimagic strength of graphs, manuscript, 2008.
  [3] D.W. Cranston, Regular bipartite graphs are antimagic, Journal of Graph Theory 60 (3) (2009) 173–182.
  [4] N. Hartsfield, G. Ringel, Perals in Graph THeory, Academic Press, INC, Boston, 1990, pp. 108–109. Revised version 1994.
  [5] G. Kaplan, A. Lev, Y. Roditty, On zero-sum partitions and anti-magic trees, Discrete Mathematics 309 (2009) 2010–2014.
  [6] Y. Liang, X. Zhu, Antimagic labeling of regular graphs, manuscript, 2012.
  [7] Y. Zhang, X. Sun, The antimagicness of the Cartesian product of graphs, Theoretical Computer Science 410 (2009) 727–735.
  [8] Subramanian Arumugam, Mirka Miller, OudonePhanalasy and Joe Ryan, Antimagic labeling of generalized pyramid graphs, ActaMathematicaSinica, English Series, 30, 2, (283).
  

  Citation
  T. Subhramaniyan and S. Suruthi, "Anti-magic labeling for Boolean graph of path BG(P_n), (n≥4)," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.306-310, 2018

• Open Access   Article

  Some Results on Contra Harmonic Mean Labeling of Graphs

  J.Rajeshni Golda, S.S.Sandhya, S. Somasundram

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.311-319, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.311319

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  Abstract
  In this paper we prove that some standard graphs like Comb, Ladder, Crown, Triangular, snake, Quadrilateral snake, Alternate Triangular snake, Alternate Triangular snake and Alternate Quadrilateral snake are Contra Harmonic mean graphs.

  Key-Words / Index Term
  Graph, Contra Harmonic mean graph, Comb, Ladder, Crown, Triangular snake, Alternate Triangular, snake, Quadrilateral snake, Alternate Quadrilateral snake

  References
  [1] J.A Bondy and Murthy, Graph Theory and Applications, NewYork(1976).
  [2] Gallian J.A. (2016). A Dynamic survey of graph labeling. The electronic Journal of Combinatorics.
  [3] Harary. F (1988) Graph Theory, Narosa Publishing House Reading New Delhi.
  [4] Somasundaram. S and Ponraj .R (2003), Mean labeling graphs, National Academy of Science letters vol.26 p210-2013.
  [5] Somasundaram.S and Ponraj.R (2003), Some results on mean graphs, Pure and Applied Mathematics Science vol.58, p29-35.
  [6] Somasundaram.S and SandhyaS.S , Harmonic mean labeling of graphs, Journal of Combinatorial Mathematics and Combinatorial Computating.
  [7] S.S.Sandhya, S. Somasundram, J.Rajeshni Golda ‘ Contra Harmonic Mean Labeling of Some Graphs’ International Journal of Contemporary Mathematical Science.
  

  Citation
  J.Rajeshni Golda, S.S.Sandhya, S. Somasundram, "Some Results on Contra Harmonic Mean Labeling of Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.311-319, 2018

• Open Access   Article

  Differential Equation Model on the Prevalence of Diabetic Neuropathy

  P. Sankar, M.S. Paulraj, J. Jayanthi and M.G. Ragunathan

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.5 , Issue.4 , pp.320-323, Aug-2018

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.320323

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  Diabetic neuropathy is the most common complication of diabetes mellitus, and can be related to Type1 as well as Type2 diabetes. This neurological impairment is not known or understood; hence the treatments are still empirical and not efficient as stated by the physicians. The purpose of this study is to discuss the population based Mathematical model of diabetic neuropathy patients. The study adopted in Ordinary Differential Equations which contains the percentage of diabetic patients with and without diabetic neuropathy. By appropriate definition of a parameter, the solution discussed the critical nature of percentage of diabetic patients with and without diabetic neuropathy is discussed for stability.

  Key-Words / Index Term
  Diabetes, Diabetic Neuropathy, Classification, Ordinary Differential Equations.

  References
  [1] Sandhya, Deepak Kumar, and Prerna Pandit; An Ordinary Differential Equation Model ofdiabetic population in NewDelhi. Indian Journal of Mathematics and Mathematical Sciences Vol. 7, No. 1, (June 2011): 45-50R.
  [2] Sarah Wild, Gojka Roglic, Anders Green, Richard Sicree, and Hilary King, (2004),Global Prevalence of Diabetes, Estimates for the Year 2000 and Projections for 2030.Diabetes Care, 27, 1047-1053.
  [3] A. Boutayeb, A.Chetouani, A. Achouyab, and E. H. Twizell, (2006), A Non-LinearPopulation Model of Diabetes Mellitus, J. Appl. Math. & Computing, 21(1), 127-139.
  [4] Jitender Nagpal, and Abhishek Bhartia, (2006), Quality of Diabetes Care in the Middle-and High-Income Group Populace, Diabetes Care, 27, 1047-1053.
  [5] Deepak Kumar, Sandhya, Anuj Kumar, and Prerna Pandit, (2009), A ComputationalModel for Diabetes Mellitus, Optimization-Journal of Research and Management, 39-43.
  

  Citation
  P. Sankar, M.S. Paulraj, J. Jayanthi and M.G. Ragunathan, "Differential Equation Model on the Prevalence of Diabetic Neuropathy," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.320-323, 2018