New contractive mappings and their fixed points in Branciari metric spaces
type: Item
instance of: scholarly article
title: New contractive mappings and their fixed points in Branciari metric spaces
zbMATH Open document ID: 1476.54114
DOI: 10.1155/2020/9491786
author: Hayel N. Saleh
author: Thabet Abdeljawad
author: M. Arif
author: Mohammad Imdad
published in: Journal of Function Spaces
publication date: 2020-07-15T00:00:00Z
review text: Summary: In this paper, we introduce the notion of generalized \(\mathcal{L}\)-contractions which enlarge the class of \(\mathcal{L}\)-contractions initiated by \textit{S.-H. Cho} [Abstr. Appl. Anal. 2018, Article ID 1327691, 6 p. (2018; Zbl 1470.54052)]. Thereafter, we also, define the notion of \(\mathcal{L}^\ast\)-contractions. Utilizing our newly introduced notions, we establish some new fixed-point theorems in the setting of complete Branciari's metric spaces, without using the Hausdorff assumption. Moreover, some examples and applications to boundary value problems of the fourth-order differential equations are given to exhibit the utility of the obtained results.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54E50
zbMATH DE Number: 7220569
zbMATH Keywords: generalized \(\mathcal{L}\)-contractions
zbMATH Keywords: \(\mathcal{L}^*\)-contractions
zbMATH Keywords: complete Branciari metric spaces
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/9491786
OpenAlex ID: W3038390312
cites work: A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces
cites work: CONTRACTIONS OVER GENERALIZED METRIC SPACES
cites work: Q3074474
cites work: Fixed point results in generalized metric spaces without Hausdorff property
cites work: On generalized metric spaces: a survey
cites work: Solutions of boundary value problems on extended-Branciari \(b\)-distance
cites work: A new generalization of the Banach contraction principle
cites work: Fixed point theorems for \(\mathcal{L}\)-contractions in generalized metric spaces
cites work: Q4978119
cites work: A new approach on coupled fixed point theory in JS-metric spaces
cites work: On \(\alpha\)-\(\psi\)-Geraghty contraction type mappings on quasi-Branciari metric spaces
cites work: Some common fixed point results in rectangular metric spaces
cites work: Generalized contractions with triangular \(\alpha\)-orbital admissible mapping on Branciari metric spaces
cites work: On common fixed points in the context of Brianciari metric spaces
cites work: Some fixed point theorems in Branciari metric spaces
cites work: Fixed points of \((\psi, \phi)\)-contractions on rectangular metric spaces
cites work: Further generalizations of the Banach contraction principle
cites work: Weak \(\theta\)-contractions and some fixed point results with applications to fractal theory
cites work: Fixed point results for generalized Theta-contractions
cites work: New fixed point results in b-rectangular metric spaces
cites work: Generalized metrics and Caristi's theorem
description: scientific article; zbMATH DE number 7220569