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.

scholarly journals Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Jian-Wen Peng ◽  
Yan Wang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems

We introduce an Ishikawa iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007).

Generalized three-step iteration schemes and common fixed points of three asymptotically quasi-nonexpansive mappings

2008 ◽  
Vol 41 (4) ◽  
Author(s):  
R. A. Rashwan ◽  
A. A. Abdel Hakim
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Convergence Theorems

AbstractIn this paper, we study strong convergence theorems for a generalized three-step iterative scheme with errors to approximate common fixed points of three asymptotically quasi-nonexpansive mappings in real Banach spaces. Our results generalize and improve upon the corresponding results in [

scholarly journals General Iterative Methods for Equilibrium Problems and Infinitely Many Strict Pseudocontractions in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Peichao Duan ◽  
Aihong Wang
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems ◽  
Pseudocontractive Mappings

We propose an implicit iterative scheme and an explicit iterative scheme for finding a common element of the set of fixed point of infinitely many strict pseudocontractive mappings and the set of solutions of an equilibrium problem by the general iterative methods. In the setting of real Hilbert spaces, strong convergence theorems are proved. Our results improve and extend the corresponding results reported by many others.

scholarly journals Multiple-Set Split Feasibility Problems forκ-Strictly Pseudononspreading Mapping in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Jing Quan ◽  
Shih-sen Chang ◽  
Xiang Zhang
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Infinite Dimensional ◽  
Split Feasibility Problems ◽  
Split Feasibility ◽  
Strictly Pseudononspreading Mapping

The purpose of this paper is to prove some weak and strong convergence theorems for solving the multiple-set split feasibility problems forκ-strictly pseudononspreading mapping in infinite-dimensional Hilbert spaces by using the proposed iterative method. The main results presented in this paper extend and improve the corresponding results of Xu et al. (2006), of Osilike et al. (2011), and of many other authors.

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