Fixed point theorems for a system of operator equations with applications

Abstract

The purpose of this paper is to present some existence and uniqueness theorems for a general system of operator equations. The abstract result generalizes some existence results obtained in [V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 7347-7355] for the case of coupled fixed point problem. We also provide an application to a system of integro-differential equations.