scholarly journals On the Convergence of Implicit Iterative Processes for Asymptotically Pseudocontractive Mappings in the Intermediate Sense

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Xiaolong Qin ◽  
Jong Kyu Kim ◽  
Tianze Wang
Keyword(s):  
Hilbert Space ◽  
Weak Convergence ◽  
Fixed Points ◽  
Iterative Process ◽  
Real Hilbert Space ◽  
Common Fixed Points ◽  
Finite Family ◽  
Strong And Weak Convergence ◽  
Pseudocontractive Mappings ◽  
Asymptotically Pseudocontractive Mappings

An implicit iterative process is considered. Strong and weak convergence theorems of common fixed points of a finite family of asymptotically pseudocontractive mappings in the intermediate sense are established in a real Hilbert space.

scholarly journals A New Approximation Method for Common Fixed Points of a Finite Family of Generalized Asymptotically Quasinonexpansive Mappings in Banach Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15
Author(s):  
Pornsak Yatakoat ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Approximation Method ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Finite Family ◽  
Strong And Weak Convergence

We introduce a new iterative scheme to approximate a common fixed point for a finite family of generalized asymptotically quasinonexpansive mappings. Several strong and weak convergence theorems of the proposed iteration in Banach spaces are established. The main results obtianed in this paper generalize and refine many known results in the current literature.

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.

scholarly journals Approximation Analysis for a Common Fixed Point of Finite Family of Mappings Which Are Asymptoticallyk-Strict Pseudocontractive in the Intermediate Sense

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
H. Zegeye ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Process ◽  
Convex Sets ◽  
Common Fixed Points ◽  
Finite Family ◽  
Important Class ◽  
Pseudocontractive Mappings ◽  
Approximation Analysis ◽  
Uniformly Continuous

We introduce an iterative process which converges strongly to a common fixed point of a finite family of uniformly continuous asymptoticallyki-strict pseudocontractive mappings in the intermediate sense fori=1,2,…,N. The projection ofx0onto the intersection of closed convex setsCnandQnfor eachn≥1is not required. Moreover, the restriction that the interior of common fixed points is nonempty is not required. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

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