Multidimensional fuzzy ϕ-contraction inequality and its application

Abstract

This paper introduces and explores the concept of fuzzy ϕ-contraction to establish the existence of n-tupled coincidence points in partially ordered GV-fuzzy metric spaces. Using the unique properties of the H-type triangular norm, we integrate this norm into GV-fuzzy metric spaces. The mappings under consideration exhibit the mixed monotone property with respect to partial ordering. Furthermore, we employ the mixed g-monotone property of mappings to analyze their behavior within the given framework. To validate our theoretical findings, we present an illustrative example, which demonstrates the higher-dimensional analysis of the ϕ-contraction principle used in our primary results. As an application, we investigate the existence of solutions for a system of second-kind Fredholm nonlinear integral equations. Employing the developed fixed-point results, we establish sufficient conditions that guarantee the solvability of such integral equations within the GV-fuzzy metric space setting.