Abstract
The purpose of this paper is to establish some strong convergence theorems for a common fixed point of two total quasi-ϕ-asymptotically nonexpansive mappings in Banach space by means of the hybrid method in mathematical programming. The results presented in this paper extend and improve on the corresponding ones announced by Martinez-Yanes and Xu (2006), Plubtieng and Ungchittrakool (2007), Qin et al. (2009), and many others.
Highlights
Let E be a smooth Banach space and let E∗ be the topological dual of E
The results presented in this paper extend and improve on the corresponding ones announced by Martinez-Yanes and Xu (2006), Plubtieng and Ungchittrakool (2007), Qin et al (2009), and many others
The main results of this paper are stated as follows
Summary
Let E be a smooth Banach space and let E∗ be the topological dual of E. The purpose of this paper is to establish some strong convergence theorems for a common fixed point of two total quasi-φasymptotically nonexpansive mappings in Banach space by means of the hybrid method in mathematical programming. Motivated and inspired by [2, 4, 10, 12,13,14,15,16,17], the purpose of this paper is to modify Halpern iteration (2) by means of both methods above for two total quasi-φ-asymptotically nonexpansive mappings and to prove the strong convergence in the framework of Banach spaces.
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