Abstract and Applied Analysis

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

Mujahid Abbas, Basit Ali, and Salvador Romaguera

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 391952, 5 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606984

Digital Object Identifier
doi:10.1155/2014/391952

Mathematical Reviews number (MathSciNet)
MR3176740

Zentralblatt MATH identifier
07022293

Citation

Abbas, Mujahid; Ali, Basit; Romaguera, Salvador. Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 391952, 5 pages. doi:10.1155/2014/391952. https://projecteuclid.org/euclid.aaa/1412606984


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