On the existence and uniqueness theorems of solutions for a class of the systems of mixed monotone operator equations with application

Abstract

By using the equivalent classes (which are called components) of a real Banach space, the existence, uniqueness and symmetric or nonsymmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. The results obtained here are a generalization of the corresponding results of Guo Dajun (1988, 1992), Pan Xingbin (1988) and Li Fuyi & Liang Zhandong(1994). As application, the results are used to study the existence and uniqueness problems of common solutions for a class of systems of nonlinear integral equations.