Some results on fixed points for a class of generalized Reich type enriched $F$-contractions with some of its application

Abstract

This article introduces a class of possibly non-continuous operators, termed generalized Reich type enriched $F$-contractions, within the framework of normed spaces. These operators generalize existing Reich type contractive mappings and $F$-contractions, thereby broadening the scope of fixed point theory to encompass more general and nonlinear settings. The article establishes several fixed point and common fixed point theorems for this class, supported by illustrative examples. Importantly, these results are applicable to the study of Volterra integral equations and systems thereof, demonstrating the practical relevance of the theoretical framework. The developed approach not only enhances the understanding of nonlinear operator behavior but also contributes to the mathematical tools available for solving integral equations that arise in applied contexts.