Strong Convergence for Hybrid ImplicitS-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings-Reference-Cited by-同舟云学术

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

Published:2014 Issue: Volume:2014 Page:1-5
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Kang Shin Min¹^ORCID,Rafiq Arif²,Ali Faisal³^ORCID,Kwun Young Chel⁴^ORCID

Affiliation:

1. Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

2. Department of Mathematics, Lahore Leads University, Lahore 54810, Pakistan

3. Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan

4. Department of Mathematics, Dong-A University, Busan 604-714, Republic of Korea

Abstract

LetKbe a nonempty closed convex subset of a real Banach spaceE, letS:K→Kbe nonexpansive, and let T:K→Kbe Lipschitz strongly pseudocontractive mappings such thatp∈FS∩FT=x∈K:Sx=Tx=xandx-Sy≤Sx-Sy and x-Ty≤Tx-Tyfor allx, y∈K. Letβnbe a sequence in0, 1satisfying (i)∑n=1∞βn=∞; (ii)limn→∞⁡βn=0.For arbitraryx0∈K, letxnbe a sequence iteratively defined byxn=Syn, yn=1-βnxn-1+βnTxn, n≥1.Then the sequencexnconverges strongly to a common fixed pointpofSandT.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/735673.pdf

Reference19 articles.

1. Nonlinear semigroups and evolution equations

2. Fixed points by a new iteration method

3. Mean value methods in iteration

4. Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces

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