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

## 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.

## Authors

C. D. Alecsa
Babes-Bolyai University, Mihail Kogalniceanu street no. 1, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Cluj-Napoca ,Romania

## Keywords

Banach algebras; (G)-convergence; (H)-convergence; differential equations; fixed points; sequeneces of contractions

## Paper coordinates

Cristian-Daniel Alecsa, Sequences of contractions on cone metric spaces over Banach algebras and applications to nonlinear systems of equations and systems of differential equations, International J. Nonlin. Anal. Appl., 10 (2019) 2, pp. 227-254,
DOI: 10.22075/ijnaa.2019.18884.2040

## PDF

##### Journal

International J. Nonlin. Anal. Appl.

##### Publisher Name

Semnan Univ., Iran

##### DOI

10.22075/ijnaa.2019.18884.2040 (not working yet)