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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Vydáno v:Abstract and Applied Analysis Ročník 2014; číslo 2014; s. 479 - 483-558
Hlavní autoři: Abbas, Mujahid, Romaguera, Salvador, Ali, Basit
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Wiley
Témata:
Algorithms
Analysis
Applied mathematics
Approximation
Approximation theory
Banach spaces
Colleges & universities
Cybernetics
Fuzzy sets
Mappings (Mathematics)
Mathematics
Set theory
United States
ISSN:1085-3375, 1687-0409
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/391952