\(F\)-convex contraction via admissible mapping and related fixed point theorems with an application
type: Item
instance of: scholarly article
title: \(F\)-convex contraction via admissible mapping and related fixed point theorems with an application
zbMATH Open document ID: 1405.54031
author: M. S. Khan
author: Yumnam Mahendra Singh
author: Shin Min Kang
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: Summary: In this paper, we introduce \(F\)-convex contraction via admissible mapping in the sense of \textit{D. Wardowski} [Fixed Point Theory Appl. 2012, Paper No. 94, 6 p. (2012; Zbl 1310.54074)] which extends convex contraction mapping of type-2 of \textit{V. I. Istratescu} [Libertas Math. 1, 151--163 (1981; Zbl 0477.54032)] and establish a fixed point theorem in the setting of metric space. Our result extends and generalizes some other similar results in the literature. As an application of our main result, we establish an existence theorem for the non-linear Fredholm integral equation and give a numerical example to validate the application of our obtained result.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 6994636
zbMATH Keywords: \(\alpha\)-admissible mapping
zbMATH Keywords: \(\alpha^\ast\)-admissible
zbMATH Keywords: \(F\)-contraction
zbMATH Keywords: \(\alpha\)-\(F\)-convex contraction
zbMATH Keywords: fixed point
zbMATH Keywords: non-linear Fredholm integral equation
MaRDI profile type: Publication
full work available at URL: math6060105
OpenAlex ID: W2808766465
cites work: Q5643278
cites work: A Generalization of Banach's Contraction Principle
cites work: Q3935134
cites work: Fixed point theorems for convex contraction mappings on cone metric spaces
cites work: Some ordered fixed point results and the property (P)
cites work: Approximate fixed point theorems for partial generalized convex contraction mappings in \(\alpha\)-complete metric spaces
cites work: Approximate fixed points of generalized convex contractions
cites work: A generalization of Istrățescu’s fixed point theorem for convex contractions
cites work: On generalized convex contractions of type-2 in b-metric and 2-metric spaces
cites work: On (α,p)-convex contraction and asymptotic regularity
cites work: Fixed points of a new type of contractive mappings in complete metric spaces
cites work: Fixed point theorems for \(\alpha\)-\(\psi\)-contractive type mappings
cites work: On \(\alpha\)-\(\psi\)-Meir-Keeler contractive mappings
cites work: α-ψ-Geraghty contraction type mappings and some related fixed point results
cites work: Some fixed point theorems for \((\alpha,\psi)\)-rational type contractive mappings
Wikidata QID: Q129637669
DOI: 10.3390/MATH6060105
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description: scientific article; zbMATH DE number 6994636