Common Coupled Fixed Foint Theorems for Nonlinear Contractive Condition on Intuitionistic Fuzzy Metric Spaces With Application to Integral Equations

Abstract

Abstract. We establish a common fixed point theorem for mappings under φ-contractive conditions on intuitionistic fuzzy metric spaces. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to validate our result.

Application of Coupled Fixed Point Technique in Solving Integral Equations on Modified Intuitionistic Fuzzy Metric Spaces

“…We extend and generalize the results of Hu [11], Hu et al [12], and Sedghi et al [10] in the settings of modified intuitionistic fuzzy metric spaces. The result is the genuine generalization of the result of Deshpande et al [13].…”

“…Remark 34. Comparing Theorem 31 in the present paper with Theorem 3.1 in [13], we can see that Theorem 31 is a genuine generalization of Theorem 3.1 in the sense that (1) we only use the completeness of ( ) or ( × );…”

“…Very recently, Deshpande et al [13] proved a common fixed point theorem for mappings under -contractive conditions on intuitionistic fuzzy metric spaces. As an application, they study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation.…”

Common Coupled Fixed Point Theorems for Two Hybrid Pairs of Mappings under φ-ψ Contraction

“…Deshpande and Handa [ 13 ] generalized and intuitionistically fuzzified the results of Gnana Bhaskar and Lakshmikantham [ 8 ], Lakshmikantham and Ćirić [ 11 ], and Luong and Thuan [ 9 ], while Deshpande et al [ 14 ] generalized and intuitionistically fuzzified the results of Berinde [ 10 ], Gnana Bhaskar and Lakshmikantham [ 8 ], Lakshmikantham and Ćirić [ 11 ], and Luong and Thuan [ 9 ]. In [ 15 ], Deshpande et al proved a common coupled fixed point theorem for mappings under φ -contractive conditions on intuitionistic fuzzy metric spaces. As an application, the existence and uniqueness of solution to a nonlinear Fredholm integral equation have been studied.…”

Common Coupled Fixed Point Theorem Under Generalized Mizoguchi-Takahashi Contraction for Hybrid Pair of Mappings Generalized Mizoguchi-Takahashi Contraction

“…Very few researcher gave attention to coupled fixed point problems for hybrid pair of mappings including [1,2,11,12,13,14,15,20,29].…”