Generalized contraction and invariant approximation results on nonconvex subsets of normed spaces
type: Item
instance of: scholarly article
title: Generalized contraction and invariant approximation results on nonconvex subsets of normed spaces
zbMATH Open document ID: 1472.47041
DOI: 10.1155/2014/391952
author: M. Abbas
author: Basit Ali
author: Salvador Romaguera
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: \textit{D. Wardowski} [Fixed Point Theory Appl. 2012, Paper No. 94, 6 p. (2012; Zbl 1310.54074)] 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.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 7022293
zbMATH Keywords: generalized \(F\)-contraction mappings
zbMATH Keywords: generalized nonexpansive mappings
zbMATH Keywords: invariant approximations
Wikidata QID: Q59037193
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/391952
OpenAlex ID: W2022535940
cites work: Boyd-Wong-type common fixed point results in cone metric spaces
cites work: On Nonlinear Contractions
cites work: Cone metric spaces and fixed point theorems of contractive mappings
cites work: A Note on Contractive Mappings
cites work: An Approach to Fixed-Point Theorems on Uniform Spaces
cites work: A fixed-point theorem for S-type operators on Banach spaces and its applications to boundary-value problems
cites work: Some fixed point theorems of the Schauder and the Krasnosel'skii type and application to nonlinear transport equations
cites work: Invarianz bei linearen Approximationen
cites work: Q5608385
cites work: Fixed point theorems and invariant approximations
cites work: A note on fixed-point theorems
cites work: Q5471260
cites work: Q3320838
cites work: An application of a fixed-point theorem to approximation theory
cites work: Q3326212
cites work: An application of a fixed point theorem to best approximation
cites work: Fixed Point Theorems for Non-Expansive Mappings on Star-Shaped Subsets of Banach Spaces
cites work: Q4881561
cites work: Fixed points of a new type of contractive mappings in complete metric spaces
cites work: Fixed and periodic points of generalized contractions in metric spaces
cites work: Q3869872
description: scientific article; zbMATH DE number 7022293