Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces

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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Main Authors: Mujahid Abbas, Basit Ali, Salvador Romaguera
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/391952
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spelling doaj-263622c8a42b4ec4af57adb1c5c499022020-11-24T21:37:54ZengHindawi LimitedAbstract 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
collection DOAJ
language English
format Article
sources DOAJ
author Mujahid Abbas
Basit Ali
Salvador Romaguera
spellingShingle Mujahid Abbas
Basit Ali
Salvador Romaguera
Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces
Abstract and Applied Analysis
author_facet Mujahid Abbas
Basit Ali
Salvador Romaguera
author_sort Mujahid Abbas
title 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_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_sort generalized contraction and invariant approximation results on nonconvex subsets of normed spaces
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
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.
url http://dx.doi.org/10.1155/2014/391952
work_keys_str_mv AT mujahidabbas generalizedcontractionandinvariantapproximationresultsonnonconvexsubsetsofnormedspaces
AT basitali generalizedcontractionandinvariantapproximationresultsonnonconvexsubsetsofnormedspaces
AT salvadorromaguera generalizedcontractionandinvariantapproximationresultsonnonconvexsubsetsofnormedspaces
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