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APPLICATION OF CONTRACTION MAPPING PRINCIPLE IN INTEGRAL EQUATION

  • Amrish Handa (Department of Mathematics, Govt. P. G. Arts and Science College)
  • Received : 2023.09.21
  • Accepted : 2023.10.06
  • Published : 2023.11.30

Abstract

In this paper, we establish some common fixed point theorems satisfying contraction mapping principle on partially ordered non-Archimedean fuzzy metric spaces and also derive some coupled fixed point results with the help of established results. We investigate the solution of integral equation and also give an example to show the applicability of our results. These results generalize, improve and fuzzify several well-known results in the recent literature.

Keywords

References

  1. S.A. Al-Mezel, H. Alsulami, E. Karapinar & A. Roldan: Discussion on multidimensional coincidence points via recent publications. Abstr. Appl. Anal. 2014 (2014), Article ID 287492. https://doi.org/10.1155/2014/287492
  2. A. Alotaibi & S.M. Alsulami: Coupled coincidence points for monotone operators in partially ordered metric spaces. Fixed Point Theory Appl. 2011 (2011), Paper No. 44. https://doi.org/10.1186/1687-1812-2011-44
  3. S.M. Alsulami: Some coupled coincidence point theorems for a mixed monotone operator in a complete metric space endowed with a partial order by using altering distance functions. Fixed Point Theory Appl. 2013 (2013), Paper No. 194. https://doi.org/10.1186/1687-1812-2013-194
  4. T.G. Bhaskar & V. Lakshmikantham: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65 (2006), no. 7, 1379-1393. https://doi.org/10.1016/j.na.2005.10.017
  5. B.S. Choudhury & A. Kundu: A coupled coincidence point results in partially ordered metric spaces for compatible mappings. Nonlinear Anal. 73 (2010), 2524-2531. https://doi.org/10.1016/j.na.2010.06.025
  6. B. Deshpande, S. Chouhan & A. Handa: Nonlinear contractive condition for generalized compatible mappings in consideration of common fixed point on fuzzy metric spaces. J. Fuzzy Math. 24 (2016), no. 3, 593-608.
  7. B. Deshpande & A. Handa: Common fixed point results for generalized compatible pair on modified intuitionistic fuzzy metric spaces. J. Fuzzy Math. 23 (2015), no. 4, 937-954.
  8. B. Deshpande & A. Handa: Application of generalized weakly compatibility in common fixed point results on fuzzy metric spaces. J. Fuzzy Math. 24 (2016), no. 1, 57-73.
  9. B. Deshpande & A. Handa: Generalized weakly compatible pair of mappings and its application in common fixed point results on modified intuitionistic fuzzy metric spaces. J. Fuzzy Math. 24 (2016), no. 1, 129-149.
  10. B. Deshpande & A. Handa: Existence of coupled coincidence point for a generalized compatible pair on partially ordered modified intuitionistic fuzzy metric spaces with applications. J. Fuzzy Math. 24 (2016), no. 3, 663-698.
  11. B. Deshpande & A. Handa: Employing generalized compatibility to prove coupled coincidence and fixed point results on fuzzy metric spaces with applications. J. Fuzzy Math. 24 (2016), no. 3, 699-730.
  12. B. Deshpande, M. Imdad & A. Handa: Common fixed point results under new condition on modified intuitionitic fuzzy metric spaces. J. Fuzzy Math. 24 (2016), no. 4, 955-976.
  13. I.M. Erhan, E. Karapinar, A. Roldan & N. Shahzad: Remarks on coupled coincidence point results for a generalized compatible pair with applications. Fixed Point Theory Appl. 2014 (2014), Paper No. 207. http://dx.doi.org/10.1186/1687-1812-2014-207
  14. A. George & P. Veeramani: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7
  15. D. Guo & V. Lakshmikantham: Coupled fixed points of nonlinear operators with applications. Nonlinear Anal. 11 (1987), no. 5, 623-632. https://doi.org/10.1016/0362-546X(87)90077-0
  16. A. Handa: Generalized (ψ, θ, ϕ)-contraction on partially ordered fuzzy metric spaces with application to the domain of words. J. Fuzzy Math. 27 (2019), no. 4, 845-873.
  17. J. Harjani, B. Lopez & K. Sadarangani: Fixed point theorems for mixed monotone operators and applications to integral equations. Nonlinear Anal. 74 (2011), 1749-1760. https://doi.org/10.1016/j.na.2010.10.047
  18. J. Harjani & K. Sadarangani: Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations. Nonlinear Anal. 72 (2010), 1188-1197. https://doi.org/10.1016/j.na.2009.08.003
  19. X. Hu: Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces. Fixed Point Theory Appl. Volume 2011, Article ID 363716, 14 pages.
  20. V. Istratescu: An Introduction to Theory of Probabilistic Metric Spaces with Applications. Ed, Tehnica, Bucuresti, 1974.
  21. I. Kramosil & J. Michalek: Fuzzy metric and statistical metric spaces. Kybernetika 11 (1975), 336-344. http://dml.cz/dmlcz/125556
  22. V. Lakshmikantham & L. Ciric: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. 70 (2009), no. 12, 4341-4349. https://doi.org/10.1016/j.na.2008.09.020
  23. N.V. Luong & N.X. Thuan: Coupled fixed points in partially ordered metric spaces and application. Nonlinear Anal. 74 (2011), 983-992. https://doi.org/10.1016/j.na.2010.09.055
  24. J.J. Nieto & R. Rodriguez-Lopez: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. 22 (2005), 223-239. https://doi.org/10.1007/s11083-005-9018-5
  25. A.C.M. Ran & M.C.B. Reurings: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Amer. Math. Soc. 132 (2004), 1435-1443.
  26. A. Razani & V. Parvaneh: Coupled coincidence point results for (ψ, α, β)-weak contractions in partially ordered metric spaces. J. Appl. Math. 2012, Article ID 496103. https://doi.org/10.1155/2012/496103
  27. B. Schweizer & A. Sklar: Statistical metric spaces. Pacific J. Math. 10 (1960), 314-334.
  28. Y. Su: Contraction mapping principle with generalized altering distance function in ordered metric spaces and applications to ordinary differential equations. Fixed Point Theory Appl. 2014 (2014), Paper No. 227. https://doi.org/10.1186/1687-1812-2014-227