scholarly journals On the convergence of some iteration processes for J-pseudomonotone mixed variational inequalities in uniformly smooth Banach spaces

2007 ◽  
Vol 46 (3-4) ◽  
pp. 557-572 ◽  
Author(s):  
A.M. Saddeek ◽  
Sayed A. Ahmed
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Uniformly Smooth ◽  
Mixed Variational Inequalities ◽  
Uniformly Smooth Banach Spaces ◽  
Iteration Processes

scholarly journals Approximating the zeros of accretive operators by the Ishikawa iteration process

1996 ◽  
Vol 1 (2) ◽  
pp. 153-167 ◽  
Author(s):  
Zhou Haiyun ◽  
Jia Yuting
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Iteration Process ◽  
Accretive Operators ◽  
Convergence Theorems ◽  
Ishikawa Iteration ◽  
Uniformly Smooth ◽  
Ishikawa Iteration Process ◽  
Uniformly Smooth Banach Spaces ◽  
Iteration Processes

Some strong convergence theorems are established for the Ishikawa iteration processes for accretive operators in uniformly smooth Banach spaces.

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 Iteration processes for approximating fixed points of operators of monotone type

1998 ◽  
Vol 57 (3) ◽  
pp. 433-445 ◽  
Author(s):  
Shih-Sen Chang ◽  
Kok-Keong Tan
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Ishikawa Iteration ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces ◽  
Iteration Processes ◽  
Monotone Type

In this paper, the unique fixed points of multi-valued and single-valued operators of monotone type are approximated by Ishikawa iteration processes or Mann and Ishikawa iteration processes with errors in uniformly smooth Banach spaces. The operators may not satisfy the Lipschitzian conditions and the domain or the range of the operators may not be bounded. The results presented improve and extend some recent results.

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