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2014 Strong Convergence for Hybrid Implicit S-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings
Shin Min Kang, Arif Rafiq, Faisal Ali, Young Chel Kwun
Abstr. Appl. Anal. 2014(SI71): 1-5 (2014). DOI: 10.1155/2014/735673

Abstract

Let K be a nonempty closed convex subset of a real Banach space E , let S : K K be nonexpansive, and let T : K K be Lipschitz strongly pseudocontractive mappings such that p F S F T = x K : S x = T x = x and x - S y S x - S y   and   x - T y T x - T y for all x ,   y K . Let β n be a sequence in 0 ,   1 satisfying (i) n = 1 β n = ; (ii) lim n β n = 0 . For arbitrary x 0 K , let x n be a sequence iteratively defined by x n = S y n ,   y n = 1 - β n x n - 1 + β n T x n ,   n 1 . Then the sequence x n converges strongly to a common fixed point p of S and T .

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Shin Min Kang. Arif Rafiq. Faisal Ali. Young Chel Kwun. "Strong Convergence for Hybrid Implicit S-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings." Abstr. Appl. Anal. 2014 (SI71) 1 - 5, 2014. https://doi.org/10.1155/2014/735673

Information

Published: 2014
First available in Project Euclid: 6 October 2014

zbMATH: 07022976
MathSciNet: MR3232859
Digital Object Identifier: 10.1155/2014/735673

Rights: Copyright © 2014 Hindawi

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Vol.2014 • No. SI71 • 2014
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