Generalized contraction and invariant approximation results on nonconvex subsets of normed spaces
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Authors
Abbas, Mujahid
Ali, Basit
Romaguera, Salvador
Journal Title
Journal ISSN
Volume Title
Publisher
Hindawi Publishing Corporation
Abstract
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.
Description
Keywords
Generalized F-contraction mappings, Fixed point result, Generalized nonexpansive mappings, Star-shaped subsets, Normed linear spaces
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Citation
Abbas, M, Ali, B & Romaguera, S 2014, 'Generalized contraction and invariant approximation results on nonconvex subsets of normed spaces', Abstract and Applied Analysis, vol. 2014, art. 391952, pp. 1-5.as