The Pb -cone metric spaces over Banach algebras with applications

Abstract

The aim of the article is to establish the structure of partial
cone b-metric spaces over Banach algebras. Topological and structural
properties are investigated of the new spaces. We also define generalized
Lipschitz mappings and give their application in fixed point theory. The
results presented in this paper substantially extend and strengthen the
results of the literature. Few examples are provided to support our conclusions and as an application we establish the existence and uniqueness
of a solution to a class of system of nonlinear integral equations.