Strong convergence theorems for Bregman quasi-asymptotically nonexpansive mappings and equilibrium problem in reflexive Banach spaces

Abstract

The purpose of this article is to propose an iteration algorithm for Bergman quasiasymptotically 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. Mathematics subject classification (2010): 47J05, 47H09, 49J25.