scholarly journals STRONG CONVERGENCE OF STRICT PSEUDO-CONTRACTIONS IN Q-UNIFORMLY SMOOTH BANACH SPACES

2015 ◽  
Vol 33 (1_2) ◽  
pp. 13-31
Author(s):  
Yonggang Pei ◽  
Fujun Liu ◽  
Qinghui Gao
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces

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 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 of modified Noor iterations

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Yongfu Su ◽  
Xiaolong Qin
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Strong Convergence Theorem ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces

In this paper, strong convergence theorem is obtained for the modified Noor iterations in the framework of uniformly smooth Banach spaces. Our results extend and improve the recent ones announced by Wittman, Kim, Xu, and some others.

scholarly journals Strong Convergence Theorems of Modified Ishikawa Iterative Method for an Infinite Family of Strict Pseudocontractions in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
Phayap Katchang ◽  
Wiyada Kumam ◽  
Usa Humphries ◽  
Poom Kumam
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Infinite Family ◽  
Strong Convergence Theorem ◽  
Mild Conditions ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces ◽  
Ishikawa Iterative Process

We introduce a new modified Ishikawa iterative process and a new W-mapping for computing fixed points of an infinite family of strict pseudocontractions mapping in the framework of q-uniformly smooth Banach spaces. Then, we establish the strong convergence theorem of the proposed iterative scheme under some mild conditions. The results obtained in this paper extend and improve the recent results of Cai and Hu 2010, Dong et al. 2010, Katchang and Kumam 2011 and many others in the literature.

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