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2012 Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces
Luo Yi Shi, Ru Dong Chen
J. Appl. Math. 2012(SI03): 1-11 (2012). DOI: 10.1155/2012/421050

Abstract

Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces are studied. Consider a nonexpansive self-mapping T of a closed convex subset C of a CAT(0) space X . Suppose that the set Fix ( T ) of fixed points of T is nonempty. For a contraction f on C and t ( 0,1 ) , let x t C be the unique fixed point of the contraction x t f ( x ) ( 1 - t ) T x . We will show that if X is a CAT(0) space satisfying some property, then { x t } converge strongly to a fixed point of T which solves some variational inequality. Consider also the iteration process { x n } , where x 0 C is arbitrary and x n + 1 = α n f ( x n ) ( 1 - α n ) T x n for n 1 , where { α n } ( 0,1 ) . It is shown that under certain appropriate conditions on α n , { x n } converge strongly to a fixed point of T which solves some variational inequality.

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Luo Yi Shi. Ru Dong Chen. "Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces." J. Appl. Math. 2012 (SI03) 1 - 11, 2012. https://doi.org/10.1155/2012/421050

Information

Published: 2012
First available in Project Euclid: 3 January 2013

MathSciNet: MR2935524
Digital Object Identifier: 10.1155/2012/421050

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI03 • 2012
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