Almost contraction mappings in cone b-metric spaces over Banach algebras

Abstract

We introduce the condition of being Cauchy for a sequence in cone b-metric spaces (cbms) over Banach algebras. Based on this result, we extend almost mappings in cone metric spaces over Banach algebras to cbms over Banach algebras and prove the related fixed point theorem. In addition, we apply our results to some applications to illustrate their usability.