Abstract and Applied Analysis

Strong Convergence for Hybrid Implicit S-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings

Shin Min Kang, Arif Rafiq, Faisal Ali, and Young Chel Kwun

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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 .

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 735673, 5 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606012

Digital Object Identifier
doi:10.1155/2014/735673

Mathematical Reviews number (MathSciNet)
MR3232859

Zentralblatt MATH identifier
07022976

Citation

Kang, Shin Min; Rafiq, Arif; Ali, Faisal; Kwun, Young Chel. Strong Convergence for Hybrid Implicit S -Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 735673, 5 pages. doi:10.1155/2014/735673. https://projecteuclid.org/euclid.aaa/1412606012


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