Fixed-Point Results for Generalized α -Admissible Hardy-Rogers’ Contractions in Cone b 2 -Metric Spaces over Banach’s Algebras with Application

Abstract

In the current manuscript, the notion of a cone ${\mathfrak{b}}_2$ -metric space over Banach’s algebra with parameter $\mathfrak{b}\underset{¯}{\succ }\mathfrak{e}$ is introduced. Furthermore, using $\alpha$ -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.