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Strong and Weak Convergence of Implicit Iterative Process with Errors for Asymptotically Nonexpansive Mappings
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F. Gu
Published/Copyright:
June 9, 2010
Abstract
The purpose of this paper is to study the weak and strong convergence of an new implicit iteration process to a common fixed point for a finite family of asymptotically nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve important known results in [Bauschke, J. Math. Anal. Appl. 202: 150–159, 1996], [Chang, Cho, Nonlinear Anal. Appl. 1: 369–382, 2003], [Goebel, Kirk, Proc. Amer. Math. Soc. 35: 171–174, 1972]–[Reich, J. Math. Anal. Appl. 75: 287–292, 1980], [Sun, J. Math. Anal. Appl. 286: 351–358, 2003]–[Zhou, Chang, Numer. Funct. Anal. Optim. 23: 911–921, 2002] and others.
Key words and phrases.: Asymptotically nonexpansive mapping; nonexpansive mapping; implicit iterative sequence with errors for a finite family; common fixed point; Opial condition; demi-closed principle; semi-compactness
Received: 2005-08-01
Revised: 2005-10-24
Published Online: 2010-06-09
Published in Print: 2006-December
© Heldermann Verlag
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Articles in the same Issue
- and Ultrafilters on ℚ and ω
- Remarks on Best Approximations in Generalized Convex Spaces
- A Note on P-Times and Time Projections
- The Apollonian Metric: The Comparison Property, Bilipschitz Mappings and Thick Sets
- On the Integral Quasicontinuity
- On Completeness of Random Transition Count for Markov Chains
- Notes on Uniqueness of Meromorphic Functions
- Strong and Weak Convergence of Implicit Iterative Process with Errors for Asymptotically Nonexpansive Mappings
- On Measurable Sierpiński-Zygmund Functions
- Extension Theorem for a Functional Equation
