The Common Solution For Equilibrium Problem And Bregman Nonexpansive Operator

This paper discusses four aspects of my reaserch,specific as follows:Firstly,I propose a new hybrid iterative scheme for finding a common solution to a finite of equilibrium problems and fixed point of Bregman totally quasi asymptotically nonexpansive operator in reflexive Banach spaces.Moreover,I prove some strong convergence theorems under suitable control conditions.Secondly,in reflexive Banach spaces,I propose a new iterative method for studying a common solution for general mixed equilibrium problem and Bregman strongly nonexpansive operators.Thirdly,the Halpern method was introduced to computing a common element for the general mixed equilibrium problem and left Bregman strongly nonexpansive operator in reflexive Banach spaces.Finally,I introduce Mann-Halpem algorithm for finding a common fixed point problem of finite family of right Bregman strongly nonexpansive operators in reflexive real Banach spaces.Moreover,I prove a strong convergence theorem under suitable control conditions.Finally,the application to a common zero of a finite family of maximal monotone mappings is given by the result.