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

Abstract

We establish a common coupled fixed point theorem for weakly compatible mappings on modified 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 demonstrate our result.

On Coincidence Point Theorem for New Contractive Condition With Application

“…On the other hand, Ding et al [7] proved coupled coincidence and common coupled fixed point theorems for generalized nonlinear contraction on partially ordered metric spaces which generalize the results of Lakshmikantham and Ciric [16]. Our fundamental sources are [2,5,6,7,8,12,13,14,15,19,20,21,22,23].…”

Some fuzzy common fixed point theorems using common limit in the range property with an application

“…As an application, they study the existence and uniqueness of the solution to integral equation. Some applications of fixed point theorems in metric or fuzzy metric theory can be seen in [2,3,4,7,9,11,12,16,17,18,25].…”

Multidimensional coincidence point results for generalized $(\psi ,\theta ,\varphi)$-contraction on ordered metric spaces

“…They also illustrated these results by proving the existence and uniqueness of the solution for periodic boundary value problems. A large number of authors established coupled fixed/coincidence point theorems by using this notion in different context, (see [1], [2], [3], [8], [9], [10], [15], [16], [23], [24], [28], [33], [35], [36]). Inspired by these papers, Berinde and Borcut [4] defined tripled fixed points and established some tripled fixed point theorems.…”