Common Fixed Point Theorems for Totally Quasi-G-Asymptotically Nonexpansive Semigroups with the Generalized f-Projection

Chunjie Wang, Yuanheng Wang

Department of Mathematics, Zhejiang Normal University, Jinhua, China.

DOI: 10.4236/am.2014.51004                

Abstract

In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator, we prove some strong convergence theorems of a new modified Halpern type hybrid iterative algorithm for the totally quasi-G-asymptotically nonexpansive semigroups in Banach space. The results presented in this paper extend and improve some corresponding ones by many others.

Keywords

Totally Quasi-G-Asymptotically Nonexpansive Semigroup; Generalized f-Projection Operator; Modified Halpern Type Hybrid Iterative Algorithm; Strong Convergence Theorem

Conflicts of Interest

The authors declare no conflicts of interest.

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