System of N fixed point operator equations with N-pseudocontractive mapping in reflexive Banach spaces

The purpose of this paper is to study the problem of the system of N fixed point operator equations with N-variables pseudo-contractive mapping. Firstly, the concept of N-variables pseudo-contractive mapping and relatively concepts of nonlinear mappings are presented in Banach spaces. Secondly, the existence theorems of solutions for the system of N fixed point operator equations with N-variables pseudo-contractive mapping are proved in reflexive Banach spaces by using the method of product spaces. In order to get the expected results, the normalized duality mapping of product Banach spaces is defined. Meanwhile the reflexivity of the product of reflexive Banach spaces and Opial’s condition of product spaces of Banach spaces are also discussed.