Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces

By Shih-sen Chang. 2006

75 citations recorded by the source corpus.

Abstract By using viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces, some sufficient and necessary conditions for the iterative sequence to converging to a common fixed point are obtained. The results presented in the paper extend and improve some recent results in [H.K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004) 279–291; H.K. Xu, Remark on an iterative method for nonexpansive mappings, Comm. Appl. Nonlinear Anal. 10 (2003) 67–75; H.H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 202 (1996) 150–159; B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957–961; J.S. Jung, Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 302 (2005) 509–520; P.L. Lions, Approximation de points fixes de contractions', C. R. Acad. Sci. Paris Ser. A 284 (1977) 1357–1359; A. Moudafi, Viscosity approximation methods for fixed point problems, J. Math. Anal. Appl. 241 (2000) 46–55; S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 128–292; R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486–491].

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9e302498b548352020ce46f510c0a6635c6ecb72

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In Computational Theory and Mathematics

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2. Naseer Shahzad
3. Nawab Hussain
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In Geometry and Topology

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In Numerical Analysis

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2. Naseer Shahzad

Citations in the corpus

• New Methods with Perturbations for Non-Expansive Mappings in Hilbert Spaces (2011, background): “Recently, iterative methods for finding fixed points of non-expansive mappings have received vast investigations due to its extensive applications in a variety of applied areas of inverse problem, partial differential equations, image recovery, and signal processing; see [1-34] and the references th”