scholarly journals Strong Convergence Theorems for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Nonself Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Liang-cai Zhao ◽  
Shih-sen Chang
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Approximation Problem ◽  
Countable Family ◽  
Convergence Theorems ◽  
Limit Condition ◽  
Asymptotically Nonexpansive ◽  
System Of Equilibrium Problems

The purpose of this paper is to introduce a class of total quasi-ϕ-asymptotically nonexpansive-nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the corresponding results announced by some authors recently.

scholarly journals An iterative process for a hybrid pair of generalized I-asymptotically nonexpansive single-valued mappings and generalized nonexpansive multi-valued mappings in Banach spaces

2018 ◽  
Vol 34 (1) ◽  
pp. 31-45
Author(s):  
ALI FARAJZADEH ◽  
◽  
PREEYANUCH CHUASUK ◽  
ANCHALEE KAEWCHAROEN ◽  
MOHAMMAD MURSALEEN ◽  
...  
Keyword(s):  
Weak Convergence ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Process ◽  
Finite Family ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Hybrid Pair

In this paper, an iterative process for a hybrid pair of a finite family of generalized I-asymptotically nonexpansive single-valued mappings and a finite family of generalized nonexpansive multi-valued mappings is established. Moreover, the weak convergence theorems and strong convergence theorems of the proposed iterative process in Banach spaces are proven. The examples are established for supporting our main results. The obtained results can be viewed as an improvement and extension of the several results in the literature.

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