Strong convergence theorems for Bregman totally quasi-asymptotically nonexpansive mappings in reflexive Banach spaces

Abstract

The purpose of this article is by using the shrinking projection method introduced by Takahashi, Kubota and Takeuchi to propose an iteration algorithm for Bregman total quasi-ϕ-asymptotically 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 and zero point problem of maximal monotone mappings in reflexive Banach spaces. The results presented in the paper improve and extend the corresponding results of Reich and Sabach (2010) [12], Suantai et al. (2012) [13], Nilsrakoo and Saejung (2011) [11], Qin et al. (2009) [5], Wang et al. (2011) [6], Su et al. (2010) [7], Martinez-Yanes and Xu (2006) [3] and others.