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2012 An Iterative Algorithm on Approximating Fixed Points of Pseudocontractive Mappings
Youli Yu
J. Appl. Math. 2012(SI03): 1-11 (2012). DOI: 10.1155/2012/341953

Abstract

Let E be a real reflexive Banach space with a uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed convex subset of E, and every nonempty closed convex bounded subset of K has the fixed point property for non-expansive self-mappings. Let f : K K a contractive mapping and T : K K be a uniformly continuous pseudocontractive mapping with F ( T ) . Let { λ n } ( 0 , 1 / 2 ) be a sequence satisfying the following conditions: (i) lim n λ n = 0 ; (ii) n = 0 λ n = . Define the sequence { x n } in K by x 0 K , x n + 1 = λ n f ( x n ) + ( 1 2 λ n ) x n + λ n T x n , for all n 0 . Under some appropriate assumptions, we prove that the sequence { x n } converges strongly to a fixed point p F ( T ) which is the unique solution of the following variational inequality: f ( p ) p , j ( z p ) 0 , for all z F ( T ) .

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Youli Yu. "An Iterative Algorithm on Approximating Fixed Points of Pseudocontractive Mappings." J. Appl. Math. 2012 (SI03) 1 - 11, 2012. https://doi.org/10.1155/2012/341953

Information

Published: 2012
First available in Project Euclid: 15 February 2012

zbMATH: 1295.47104
MathSciNet: MR2846451
Digital Object Identifier: 10.1155/2012/341953

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI03 • 2012
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