Fixed-Point Results for Generalized α-Admissible Hardy-Rogers’ Contractions in Cone b2-Metric Spaces over Banach’s Algebras with Application

In the current manuscript, the notion of a cone b2-metric space over Banach’s algebra with parameter b≻¯e is introduced. Furthermore, using α-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.