scholarly journals Strong and Weak Convergence Theorems for an Infinite Family of Lipschitzian Pseudocontraction Mappings in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Shih-sen Chang ◽  
Xiong Rui Wang ◽  
H. W. Joseph Lee ◽  
Chi Kin Chan
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Infinite Family ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Pseudocontractive Mappings ◽  
Iteration Processes ◽  
Implicit Iteration

The purpose of this paper is to study the strong and weak convergence theorems of the implicit iteration processes for an infinite family of Lipschitzian pseudocontractive mappings in Banach spaces.

scholarly journals Strong Convergence Theorems for Variational Inequalities and Common Fixed-Point Problems Using Relaxed Mann Implicit Iteration Methods

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 424
Author(s):  
Lu-Chuan Ceng ◽  
Meijuan Shang
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
General System ◽  
Convergence Theorems ◽  
Pseudocontractive Mappings ◽  
Convex Feasibility ◽  
Uniformly Convex Banach Spaces ◽  
Asymptotically Nonexpansive ◽  
Iteration Methods ◽  
Implicit Iteration

Mann-like iteration methods are significant to deal with convex feasibility problems in Banach spaces. We focus on a relaxed Mann implicit iteration method to solve a general system of accretive variational inequalities with an asymptotically nonexpansive mapping in the intermediate sense and a countable family of uniformly Lipschitzian pseudocontractive mappings. More convergence theorems are proved under some suitable weak condition in both 2-uniformly smooth and uniformly convex Banach spaces.

scholarly journals Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces

2010 ◽  
Vol 42 (1) ◽  
pp. 19-30
Author(s):  
Isa Yildirim ◽  
Murat Özdemir
Keyword(s):  
Weak Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Uniformly Convex Banach Spaces

In this paper, we consider a composite iterative algorithm for approximating common fixed points of two nonself asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.

scholarly journals On Picard–Krasnoselskii Hybrid Iteration Process in Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-5 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Kifayat Ullah ◽  
Junaid Ahmad
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Numerical Example ◽  
Strong And Weak Convergence ◽  
Convergence Results ◽  
Krasnoselskii Iteration ◽  
Iteration Processes

In this research, we prove strong and weak convergence results for a class of mappings which is much more general than that of Suzuki nonexpansive mappings on Banach space through the Picard–Krasnoselskii hybrid iteration process. Using a numerical example, we prove that the Picard–Krasnoselskii hybrid iteration process converges faster than both of the Picard and Krasnoselskii iteration processes. Our results are the extension and improvement of many well-known results of the literature.

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