Application Of Iterative Method To Equilibrium Problem Variational Inequality Problem And Zero Problem

The fixed point theory of Nonlinear Operator is one of the most important parts of the Nonlinear Functional Analysis.Several new iterative algorithms are proposed to approximate solution of variational inequality,common elements of the set of common fixed points of a family of quasi-?-nonexpansive mappings,the set of solutions of an equilibrium problem,and the set of common zero points of a family of maximal monotone operators in this paper.Several strong convergence theorems of fixed points are proved by using new analysis techniques.The results of this paper improve and extend recent some relative result.The main content of this paper is as follows:The first part: A new composite projection method is proposed to approximate solution of variational inequalities,a strong convergence theorem of solution of variational inequalities is proved by using new the generalized projection methd and new analysis techniques in the setting of uniformly convex,and uniformly smooth Banach spaces with the K-K property.The second part: A new shrinking projection method is proposed to approximate common elements of the set of common fixed points of a family of quasi-?-nonexpansive mappings,the set of solutions of an equilibrium problem and the set of common zero points of a family of maximal monotone operators,A strong convergence theorem of common elements is proved by using new analysis techniques in the setting of strictly convex,and uniformly smooth Banach spaces with the K-K property.As applications,the problem of finding a solution of a variational inequality is considered.