Multidimensional fuzzy ϕ-contraction inequality and its application

• Published in: Journal of inequalities and applications Vol. 2025; no. 1; pp. 77 - 19
• Main Authors: Patel, Uma Devi, Chandra, Vineeta, Moussaoui, Abdelhamid, Radenović, Stojan
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 23.06.2025; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Dimensional analysis; GV-fuzzy metric space; Integral equations; Mathematics; Mathematics and Statistics; Metric space; Mixed g-monotone property; n-tupled coincidence points; Variables; ϕ-contraction; contraction; monotone property; Mixed; tupled coincidence points; fuzzy metric space
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-025-03319-1

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.