The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings

The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings

Recently, Basha (2011) established the best proximity point theorems for proximal contractions of the first and second kinds which are extension of Banach's contraction principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the notions of proximal contract...

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Main Authors: Wutiphol Sintunavarat, Poom Kumam
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/375604
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spelling doaj-43893a90a13244509e3f0415cef184e62020-11-24T22:13:38ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/375604375604The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction MappingsWutiphol Sintunavarat0Poom Kumam1Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, ThailandRecently, Basha (2011) established the best proximity point theorems for proximal contractions of the first and second kinds which are extension of Banach's contraction principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the notions of proximal contractions of the first and second kinds which are more general than the notion of self-contractions, establish the existence of an optimal approximate solution theorems for these non-self-mappings, and also give examples to validate our main results.http://dx.doi.org/10.1155/2013/375604
collection DOAJ
language English
format Article
sources DOAJ
author Wutiphol Sintunavarat
Poom Kumam
spellingShingle Wutiphol Sintunavarat
Poom Kumam
The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings
Abstract and Applied Analysis
author_facet Wutiphol Sintunavarat
Poom Kumam
author_sort Wutiphol Sintunavarat
title The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings
title_short The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings
title_full The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings
title_fullStr The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings
title_full_unstemmed The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings
title_sort existence theorems of an optimal approximate solution for generalized proximal contraction mappings
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description Recently, Basha (2011) established the best proximity point theorems for proximal contractions of the first and second kinds which are extension of Banach's contraction principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the notions of proximal contractions of the first and second kinds which are more general than the notion of self-contractions, establish the existence of an optimal approximate solution theorems for these non-self-mappings, and also give examples to validate our main results.
url http://dx.doi.org/10.1155/2013/375604
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AT poomkumam theexistencetheoremsofanoptimalapproximatesolutionforgeneralizedproximalcontractionmappings
AT wutipholsintunavarat existencetheoremsofanoptimalapproximatesolutionforgeneralizedproximalcontractionmappings
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