Best Proximal Coupled Fixed Point Results on Fuzzy Metric Spaces Using C-Class Functions with an Application

In this paper, we introduce the notion of cyclic coupled proximal type fuzzy contraction (CCPTF-contraction) mappings in fuzzy metric spaces (FM-spaces). The condition of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>C</mml:mi> </mml:math> -class functions is used to establish some strong coupled proximal point (SCPP) results under the CCPTF-contraction mappings. The concept of closeness and the triangular condition of fuzzy metric is considered to prove our main results. We establish an illustrative example to support our work. In addition, we present an application of nonlinear integral equations (NIEs) to unify our work. This new concept of best proximal coupled fixed point results on FM-spaces with application will play a very best role for researchers in the theory of fixed point.