Fixed point methodologies for A-contraction mappings over C*-algebra with applications

Abstract

This paper delves into the fundamental and versatile field of fixed point theory within functional analysis. Given its wide-ranging applications, numerous researchers have explored various generalizations and extensions of distance spaces using this theory. Our primary objective is to establish novel fixed point results for ˆA-contraction mappings in Banach spaces over C*-algebras. Our theorems unify and extend several existing results in the literature. To illustrate the practical significance of our theoretical findings, we provide illustrative examples and applications to the Urysohn integral equation and nonlinear fractional differential equation. These applications demonstrate the versatility of our approach in solving a broad spectrum of problems.