Iterative Approximation Of Fixed Point For Non-expansive Mappings And Fixed Point Theorems For Bregman Non-spreading Operators

The problem of iterative approximation of non-expansive mappings and the problem of existence of fixed point for Bregman non-spreading operators are dis-cussed in this paper, the paper contains three parts as following:In charter one, the background of fixed point theory, main contents that we will discuss and significance are introduced.In charter two, the problem of iterative approximation of fixed point of non-expansive mapping is discussed in a Hilbert space. An iterative scheme about finite non-expansive mappings and two equilibrium problems is constructed, and under certain conditions the iterative sequence strongly converges to the common element of sets of fixed points of finite non-expansive mappings and sets of solutions of two equilibrium problems. The conclusions of this paper extend and improve the relevant results of some references.In charter three, the conception of Bregman non-spreading operator is intro-duced in a real reflexive Banach space, and by the properties of Bregman distance function and Bregman non-spreading operator some fixed point theorems for Breg-man non-spreading operator are proved.