Class Of Nonlinear Operator Fixed Point Problem

Fixed point theory is an important part of nonlinear functional analysis, which has rapid and intense connection with many branches of modern mathematics. It especially plays an important role in the problem of existence and uniqueness of establishing the solution for various types of equation (including all types of linear or non-linear, deterministic or non-deterministic differential equations, integral equations and a variety of operator equations).In this paper the existence of fixed point problems for nonlinear operator is studied; several new fixed-point theorem are established and some related known work is extended and improved.The main thesis are as follows:A class of the existence for fixed point problems of monotone operators is studied by using the real cone theory in Banach space, especially the existence of conditions of fixed point problems for multi-valued monotone operator are discussed and some corresponding fixed point theory of monotone operators are obtained.By using the real cone theory in Banach space and the iterative technique, the existence question of common fixed point for decreasing operators is investigated, and some common fixed point theorems are deduced.The existence condition of common fixed point and its structure for two expansive mappings are discussed by using the iterative technique, and two common fixed point theorems for a pair of expansive mappings are gotten.