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2013 Iterative Methods for Pseudocontractive Mappings in Banach Spaces
Jong Soo Jung
Abstr. Appl. Anal. 2013(SI01): 1-7 (2013). DOI: 10.1155/2013/643602

Abstract

Let E a reflexive Banach space having a uniformly Gâteaux differentiable norm. Let C be a nonempty closed convex subset of E , T : C C a continuous pseudocontractive mapping with F ( T ) , and A : C C a continuous bounded strongly pseudocontractive mapping with a pseudocontractive constant k ( 0,1 ) . Let { α n } and { β n } be sequences in ( 0,1 ) satisfying suitable conditions and for arbitrary initial value x 0 C , let the sequence { x n } be generated by x n = α n A x n + β n x n - 1 + ( 1 - α n - β n ) T x n , n 1 . If either every weakly compact convex subset of E has the fixed point property for nonexpansive mappings or E is strictly convex, then { x n } converges strongly to a fixed point of T , which solves a certain variational inequality related to A .

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Jong Soo Jung. "Iterative Methods for Pseudocontractive Mappings in Banach Spaces." Abstr. Appl. Anal. 2013 (SI01) 1 - 7, 2013. https://doi.org/10.1155/2013/643602

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 06209386
MathSciNet: MR3039129
Digital Object Identifier: 10.1155/2013/643602

Rights: Copyright © 2013 Hindawi

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