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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Language: | English |
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Wiley
2012-01-01
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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. |
format | Article |
id | doaj-art-1a97e763ae954bec842dde6c9991dbc1 |
institution | Kabale University |
issn | 1110-757X 1687-0042 |
language | English |
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 |