STRONG CONVERGENCE THEOREMS FOR BREGMAN QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPINGS AND EQUILIBRIUM PROBLEM IN REFLEXIVE BANACH SPACES

摘要

The purpose of this article is to propose an iteration algorithm for Bergman quasi-asymptotic ally nonexpansive mapping to have the strong convergence under a limit condition only in the framework of reflexive Banach spaces. As applications, we apply our results to a system of equilibrium problems. The results presented in the paper improve and extend the corresponding results of Reich and Sabach [Nonlinear Anal. 73 (2010),122-135], Suantai et al. [Comput. Math. Appl. 64 (2012), 489-499],Nilsrakoo and Saejung [Appl. Math. Comput. 217:14 (2011), 6577-6586], Qin et al. [Applied Math Letters, 22 (2009), 1051-1055], Wang et al. [J. Comput. Appl. Math., 235 (2011), 2364-2371], Su et al. [Nonlinear Anal. 73(2010), 390-3906], Nartinez-Yanes et al. [Nonlinear Anal., 64 (2006), 2400-2411] and others.