A fixed point theorem for a system of Pachpatte operator equations

Abstract

In this paper, we investigate sufficient conditions for the existence of solutions to the system

{Tx=x,

alpha(i)(x)=0(E), i = 1,2, ... r, where 0(E) is the zero vector of E, and alpha(i) : E -> E i = 1, 2, ... , r are mappings, T is a mapping satisfying the Pachpatte-contraction.