scholarly journals Weak and strong convergence theorems of a multistep iteration to a common fixed point of a family of nonself asymptotically nonexpansive mappings in banach spaces

Cubo (Temuco) ◽  
2012 ◽  
Vol 14 (3) ◽  
pp. 143-166
Author(s):  
Shrabani Banerjee ◽  
Binayak S Choudhury
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

scholarly journals Weak and strong convergence theorems for three Suzuki’s generalized nonexpansive mappings

2021 ◽  
Vol 110 (124) ◽  
pp. 121-129
Author(s):  
Seyit Temir
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Weak And Strong Convergence ◽  
Convergence Theorems

We introduce a new iterative scheme for finding a common fixed point of three Suzuki?s generalized nonexpansive mappings in Banach spaces. We establish weak and strong convergence theorems for three Suzuki?s generalized nonexpansive mappings. The results obtained extend and improve the recent ones announced by Ali et al., Maniu and Thakur et al..

scholarly journals Strong Convergence Theorems for Two Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xi-bing He ◽  
Xiao-jian Hui ◽  
Hui Xing
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Mathematical Programming ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Hybrid Method ◽  
Nonexpansive Mappings ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

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.

scholarly journals Weak and Strong Convergence Theorems for Finite Families of Asymptotically Quasi-Nonexpansive Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lei Deng ◽  
Juan Xiao
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Iteration Sequence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Finite Step

A finite-step iteration sequence for two finite families of asymptotically nonexpansive mappings is introduced and the weak and strong convergence theorems are proved in Banach space. The results presented in the paper generalize and unify some important known results of relevant scholars.

scholarly journals Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings

2004 ◽  
Vol 2004 (37) ◽  
pp. 1965-1971 ◽  
Author(s):  
Hafiz Fukhar-ud-din ◽  
Safeer Hussain Khan
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Weak And Strong Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
The Common

A two-step iterative scheme with errors has been studied to approximate the common fixed points of two asymptotically nonexpansive mappings through weak and strong convergence in Banach spaces.

scholarly journals Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohammed Ali Alghamdi ◽  
Naseer Shahzad ◽  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Finite Family ◽  
Monotone Mappings ◽  
Reflexive Banach Spaces ◽  
Convergence Theorems

We study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces. As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common solution of a finite family equilibrium problem and a common zero of a finite family of maximal monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

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