Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications

The aim of this paper is to introduce an iterative algorithm for finding a common solution of the sets (A+M2)−1(0) and (B+M1)−1(0), where M is a maximal accretive operator in a Banach space and, by using the proposed algorithm, to establish some strong convergence theorems for common solutions of th...

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Main Authors: Uamporn Witthayarat, Yeol Je Cho, Poom Kumam
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/185104
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author Uamporn Witthayarat
Yeol Je Cho
Poom Kumam
author_facet Uamporn Witthayarat
Yeol Je Cho
Poom Kumam
author_sort Uamporn Witthayarat
collection DOAJ
description The aim of this paper is to introduce an iterative algorithm for finding a common solution of the sets (A+M2)−1(0) and (B+M1)−1(0), where M is a maximal accretive operator in a Banach space and, by using the proposed algorithm, to establish some strong convergence theorems for common solutions of the two sets above in a uniformly convex and 2-uniformly smooth Banach space. The results obtained in this paper extend and improve the corresponding results of Qin et al. 2011 from Hilbert spaces to Banach spaces and Petrot et al. 2011. Moreover, we also apply our results to some applications for solving convex feasibility problems.
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institution Kabale University
issn 1110-757X
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publishDate 2012-01-01
publisher Wiley
record_format Article
series Journal of Applied Mathematics
spelling doaj-art-1a97e763ae954bec842dde6c9991dbc12025-02-03T06:44:34ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/185104185104Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with ApplicationsUamporn Witthayarat0Yeol Je Cho1Poom Kumam2Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, ThailandDepartment of Mathematics Education and RINS, Gyeongsang National University, Chinju 660-701, Republic of KoreaDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, ThailandThe aim of this paper is to introduce an iterative algorithm for finding a common solution of the sets (A+M2)−1(0) and (B+M1)−1(0), where M is a maximal accretive operator in a Banach space and, by using the proposed algorithm, to establish some strong convergence theorems for common solutions of the two sets above in a uniformly convex and 2-uniformly smooth Banach space. The results obtained in this paper extend and improve the corresponding results of Qin et al. 2011 from Hilbert spaces to Banach spaces and Petrot et al. 2011. Moreover, we also apply our results to some applications for solving convex feasibility problems.http://dx.doi.org/10.1155/2012/185104
spellingShingle Uamporn Witthayarat
Yeol Je Cho
Poom Kumam
Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications
Journal of Applied Mathematics
title Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications
title_full Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications
title_fullStr Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications
title_full_unstemmed Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications
title_short Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications
title_sort convergence of an iterative algorithm for common solutions for zeros of maximal accretive operator with applications
url http://dx.doi.org/10.1155/2012/185104
work_keys_str_mv AT uampornwitthayarat convergenceofaniterativealgorithmforcommonsolutionsforzerosofmaximalaccretiveoperatorwithapplications
AT yeoljecho convergenceofaniterativealgorithmforcommonsolutionsforzerosofmaximalaccretiveoperatorwithapplications
AT poomkumam convergenceofaniterativealgorithmforcommonsolutionsforzerosofmaximalaccretiveoperatorwithapplications