scholarly journals Approximating fixed points of Φ-hemicontractive mappings by the Ishikawa iteration process with errors in uniformly smooth Banach spaces

1998 ◽  
Vol 36 (2) ◽  
pp. 13-21 ◽  
Author(s):  
Zhenyu Huang
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Iteration Process ◽  
Ishikawa Iteration ◽  
Uniformly Smooth ◽  
Ishikawa Iteration Process ◽  
Uniformly Smooth Banach Spaces ◽  
Hemicontractive Mappings

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 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.

MODIFIED HALPERN ITERATIVE ALGORITHM FOR NONEXPANSIVE MAPPINGS II

2011 ◽  
Vol 04 (04) ◽  
pp. 683-694
Author(s):  
Mengistu Goa Sangago
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Convergence Conditions ◽  
Uniformly Smooth ◽  
Additional Control ◽  
Uniformly Smooth Banach Spaces

Halpern iterative algorithm is one of the most cited in the literature of approximation of fixed points of nonexpansive mappings. Different authors modified this iterative algorithm in Banach spaces to approximate fixed points of nonexpansive mappings. One of which is Yao et al. [16] modification of Halpern iterative algorithm for nonexpansive mappings in uniformly smooth Banach spaces. Unfortunately, some deficiencies are found in the Yao et al. [16] control conditions imposed on the modified iteration to obtain strong convergence. In this paper, counterexamples are constructed to prove that the strong convergence conditions of Yao et al. [16] are not sufficient and it is also proved that with some additional control conditions on the parameters strong convergence of the iteration is obtained.

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).

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