Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces
Wardowski (2012) introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle. In this paper, we introduce a notion of generalized F-contraction mappings which is used to prove a fixed point result for gene...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/391952 |
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| _version_ | 1850229012174995456 |
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| author | Mujahid Abbas Basit Ali Salvador Romaguera |
| author_facet | Mujahid Abbas Basit Ali Salvador Romaguera |
| author_sort | Mujahid Abbas |
| collection | DOAJ |
| description | Wardowski (2012) introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle. In this paper, we introduce a notion of generalized F-contraction mappings which is used to prove a fixed point result for generalized nonexpansive mappings on star-shaped subsets of normed linear spaces. Some theorems on invariant approximations in normed linear spaces are also deduced. Our results extend, unify, and generalize comparable results in the literature. |
| format | Article |
| id | doaj-art-263622c8a42b4ec4af57adb1c5c49902 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-263622c8a42b4ec4af57adb1c5c499022025-08-20T02:04:21ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/391952391952Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed SpacesMujahid Abbas0Basit Ali1Salvador Romaguera2Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria 0002, South AfricaDepartment of Mathematics, Syed Babar Ali School of Science and Engineering, Lahore University of Management Sciences, Lahore 54792, PakistanInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera s/n, 46022 Valencia, SpainWardowski (2012) introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle. In this paper, we introduce a notion of generalized F-contraction mappings which is used to prove a fixed point result for generalized nonexpansive mappings on star-shaped subsets of normed linear spaces. Some theorems on invariant approximations in normed linear spaces are also deduced. Our results extend, unify, and generalize comparable results in the literature.http://dx.doi.org/10.1155/2014/391952 |
| spellingShingle | Mujahid Abbas Basit Ali Salvador Romaguera Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces Abstract and Applied Analysis |
| title | Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces |
| title_full | Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces |
| title_fullStr | Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces |
| title_full_unstemmed | Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces |
| title_short | Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces |
| title_sort | generalized contraction and invariant approximation results on nonconvex subsets of normed spaces |
| url | http://dx.doi.org/10.1155/2014/391952 |
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