Sequences of contractions on cone metric spaces over Banach algebras and applications to nonlinear systems of equations and systems of differential equations

TL;DR

This paper develops new fixed point results for sequences of contractions in cone metric spaces over Banach algebras and applies these to solve nonlinear systems of differential and functional equations.

Contribution

It introduces novel fixed point theorems for sequences of contractions in cone metric spaces over Banach algebras, extending classical results.

Findings

New fixed point results for sequences of contractions

Applications to nonlinear differential systems

Examples illustrating the new concepts

Abstract

It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present paper represents the development of some fixed point results regarding sequences of contractions in the setting of cone metric spaces over Banach algebras. Furthermore, some examples are given in order to strengthen our new concepts. Also, based on the powerful notion of a cone metric space over a Banach algebra, we present important applications to systems of differential equations and coupled functional equations, respectively, that are linked to the concept of sequences of contractions.