STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEM AND BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES

doi:10.1016/S0252-9602(16)30079-0

Abstract

Abstract:

In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result.

Key words: equilibrium problem, Bregman totally quasi-asymptotically nonexpansive mapping, Bregman distance, reflexive Banach space

CLC Number:

26A18

Sheng ZHU, Jianhua HUANG. STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEM AND BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES[J].Acta mathematica scientia,Series B, 2016, 36(5): 1433-1444.

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