Fixed point of subadditive maps and some non-linear integral equations

TL;DR

This paper extends fixed point results for subadditive maps in Banach algebra-valued function spaces and applies these findings to establish existence and uniqueness of solutions for certain nonlinear integral equations.

Contribution

It generalizes previous fixed point theorems to subadditive separating maps on Banach algebra-valued function spaces and applies these to nonlinear integral equations.

Findings

Extended fixed point results for subadditive separating maps.

Provided conditions for unique fixed points of strongly subadditive maps.

Proved existence and uniqueness of solutions for specific nonlinear integral equations.

Abstract

In this paper, first some results of [5] are extended for subadditive separating maps between C(X;E) and C(Y;E), such that E is a unital Banach algebra. Then we give some conditions under which a strongly subadditive map has a unique fixed point. Finally as an application the existence and uniqueness of solution for a nonlinear integral equation is discussed.