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

Mujahid Abbas, Basit Ali and Salvador Romaguera

Abstract and Applied Analysis, 2014, vol. 2014, 1-5

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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:391952

DOI: 10.1155/2014/391952

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