Separate families of fuzzy dominated nonlinear operators with applications

Abstract

This paper presents novel fixed-point results for two distinct families of fuzzy-dominated operators satisfying a generalized nonlinear contraction condition on a closed ball in a complete strong b-metric-like space. Our research introduces innovative fixed-point theorems for separate families of ordered fuzzy-dominated mappings in ordered complete strong b-metric-like spaces. Two different kinds of mappings are used in our methodology: a class of fuzzy-dominated mappings and a class of strictly non-decreasing mappings. Furthermore, we establish new fixed-point results for fuzzy-graph-dominated contractions. To substantiate our findings, we provide both rigorous and illustrative examples. We demonstrate the uniqueness of our results by applying them to obtain common solutions for fractional differential equations and fuzzy Volterra integral equations.