Strong convergence theorems for asymptotically nonexpansive semigroups in Hilbert spaces

1998 ◽  
Vol 34 (1) ◽  
pp. 87-99 ◽  
Author(s):  
Naoki Shioji ◽  
Wataru Takahashi
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorems ◽  
Nonexpansive Semigroups ◽  
Asymptotically Nonexpansive

scholarly journals Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Juguo Su ◽  
Yuchao Tang ◽  
Liwei Liu
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Hybrid Algorithm ◽  
Nonexpansive Mappings ◽  
Iteration Scheme ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Iteration Methods ◽  
Mann’S Iteration

The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.

scholarly journals The Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive Mappings in Hilbert Spaces

2021 ◽  
Vol 1 (1) ◽  
pp. 19-33
Author(s):  
Sang B Mendy ◽  
John T Mendy ◽  
Alieu Jobe
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Minimization Problem ◽  
Nonexpansive Mappings ◽  
Convex Minimization ◽  
Convex Minimization Problem ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

The generalized viscosity implicit rules of nonexpansive asymptotically mappings in Hilbert spaces are considered. The strong convergence theorems of the rules are proved under certain assumptions imposed on the sequences of parameters. An application of it in the convex minimization problem is considered. The results presented in this paper improve and extend some recent corresponding results in the literature.

scholarly journals Convergence Theorems of a General Composite Iterative Method for Nonexpansive Semigroups in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
Pitipong Sunthrayuth ◽  
Kriengsak Wattanawitoon ◽  
Poom Kumam
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Iteration Scheme ◽  
Convergence Theorems ◽  
Nonexpansive Semigroups

We introduce a general composite iterative scheme for nonexpansive semigroups in Banach spaces. We establish some strong convergence theorems of the general iteration scheme under different control conditions. The results presented in this paper improve and extend the corresponding results of Marino and Xu (2006), and others, from Hilbert spaces to Banach spaces.

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