Generalized contraction and invariant approximation results on nonconvex subsets of normed spaces

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Authors

Abbas, Mujahid
Ali, Basit
Romaguera, Salvador

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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.

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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