scholarly journals Explicit averaging cyclic algorithm for common fixed points of a finite family of asymptotically strictly pseudocontractive mappings in q-uniformly smooth Banach spaces

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Ying Zhang ◽  
Zhiwei Xie
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Common Fixed Points ◽  
Finite Family ◽  
Pseudocontractive Mappings ◽  
Uniformly Smooth ◽  
Cyclic Algorithm ◽  
Uniformly Smooth Banach Spaces ◽  
Asymptotically Strictly Pseudocontractive Mappings ◽  
Strictly Pseudocontractive Mappings

scholarly journals Strong convergence theorems for fixed points of pseudo-contractive semigroup

2007 ◽  
Vol 76 (3) ◽  
pp. 441-452 ◽  
Author(s):  
Xue-Song Li ◽  
Nan-Jing Huang
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Common Fixed Points ◽  
Nonexpansive Semigroup ◽  
Uniformly Smooth ◽  
Uniformly Convex Banach Spaces ◽  
Special Cases ◽  
Uniformly Smooth Banach Spaces ◽  
Iteration Processes ◽  
Implicit Iteration

We study some convergence of two kinds of implicit iteration processes for approximating common fixed points of a pseudo-contractive semigroup in uniformly convex Banach spaces with uniformly Gateaux differential norms. As special cases, we get some convergence of the implicit iteration processes for approximating common fixed points of a nonexpansive semigroup in uniformly smooth Banach spaces and give a positive answer to an open problem proposed by Xu in Bull. Austral. Math. Soc. (2005). The results presented in this paper generalise some corresponding results from Osilike in Panamer. Math. J. (2004), Suzuki in Proc. Amer. Math. Soc. (2002) and Xu in Bull. Austral. Math. Soc. (2005).

scholarly journals Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities withk-Strict Pseudocontractions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qian-Fen Gong ◽  
Dao-Jun Wen
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Fixed Points ◽  
Convergence Analysis ◽  
Common Fixed Points ◽  
Finite Family ◽  
Steepest Descent ◽  
Descent Methods ◽  
Pseudocontractive Mappings ◽  
Strictly Pseudocontractive Mappings

We modify the relaxed hybrid steepest-descent methods to the case of variational inequality for finding a solution over the set of common fixed points of a finite family of strictly pseudocontractive mappings. The strongly monotone property defined on cost operator was extended to relaxed cocoercive in convergence analysis. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors.

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