Generalized Reich-Ćirić-Rus-type and Kannan-type contractions in cone \(b\)-metric spaces over Banach algebras
type: Item
instance of: scholarly article
title: Generalized Reich-Ćirić-Rus-type and Kannan-type contractions in cone \(b\)-metric spaces over Banach algebras
zbMATH Open document ID: 1477.54086
DOI: 10.1155/2021/7549981
author: Yan Han
author: Shaoyuan Xu
published in: Journal of Mathematics
publication date: 2021-11-25T00:00:00Z
review text: Summary: In this paper, we firstly introduce the generalized Reich-Ćirić-Rus-type and Kannan-type contractions in cone \(b\)-metric spaces over Banach algebras and then obtain some fixed point theorems satisfying these generalized contractive conditions, without appealing to the compactness of \(X\). Secondly, we prove the existence and uniqueness results for fixed points of asymptotically regular mappings with generalized Lipschitz constants. The continuity of the mappings is deleted or relaxed. At last, we prove that the completeness of cone \(b\)-metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in \(X\). Our results greatly extend several important results in the literature. Moreover, we present some nontrivial examples to support the new concepts and our fixed point theorems.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 7433561
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/7549981
OpenAlex ID: W3202103877
cites work: Q5610908
cites work: Some Remarks Concerning Contraction Mappings
cites work: A Generalization of Banach's Contraction Principle
cites work: Fixed point theorems for Kannan type mappings
cites work: On Kannan-Type Contractive Mappings
cites work: Some fixed point theorems for generalized Kannan type mappings in b-metric spaces
cites work: Q3983330
cites work: Q4884981
cites work: Multivalued fractals in \(b\)-metric spaces
cites work: KKM mappings in cone \(b\)-metric spaces
cites work: Cone metric spaces and fixed point theorems of contractive mappings
cites work: Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings
cites work: Some fixed point results of generalized Lipschitz mappings on cone \(b\)-metric spaces over Banach algebras
cites work: Q4598688
cites work: Some new theorems on \(c\)-distance without continuity in cone metric spaces over Banach algebras
cites work: Remarks on asymptotic regularity and fixed points
cites work: A note on the fixed point theorem of Górnicki
cites work: Q4340096
cites work: Some notes on the paper ``Cone metric spaces and fixed point theorems of contractive mappings''
cites work: On paracompactness in cone metric spaces
cites work: Dugundji's theorem for cone metric spaces
cites work: The solution by iteration of nonlinear functional equations in Banach spaces
cites work: Some topological properties and fixed point results in cone metric spaces over Banach algebras
cites work: Various extensions of Kannan's fixed point theorem
description: scientific article; zbMATH DE number 7433561