Strong Convergence Theorems for a Generalized Mixed Equilibrium Problem and a Family of Total Quasi--Asymptotically Nonexpansive Multivalued Mappings in Banach Spaces

The main purpose of this paper is by using a hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a infinite family of total quasi--asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results announced by some authors

APPROXIMATING COMMON ELEMENTS OF FIXED POINTS OF BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPINGS AND SOLUTIONS OF A SYSTEM OF GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN REFLEXIVE BANACH SPACES

In this paper, we introduce a hybrid iterative method for approximating common elements of common fixed points of a finite family of Bregman totally quasiasymptotically nonexpansive mappings and solutions of a finite system of generalized mixed equilibrium problems. After that, a strong convergence result for the proposed iterative method is established and proved in reflexive Banach spaces. By this result, we get some convergence results for generalized mixed equilibrium problems in reflexive Banach spaces. Furthermore, we give a numerical example to illustrate the obtained results. 

On Asymptotically Quasi-φ-Nonexpansive Mappings in the Intermediate Sense

A projection iterative process is investigated for the class of asymptotically quasi-φ-nonexpansive mappings in the intermediate sense. Strong convergence theorems of common fixed points of a family of asymptotically quasi-φ-nonexpansive mappings in the intermediate sense are established in the framework of Banach spaces