Correction to: Some generalizations for ( α − ψ , ϕ ) $(\alpha-\psi,\phi)$ -contractions in b-metric-like spaces and an application

Correction to: Some generalizations for ( α − ψ , ϕ ) $(\alpha-\psi,\phi)$ -contractions in b-metric-like spaces and an application

Abstract In the publication of this article [Fixed Point Theory Appl. 2017:26, 2017], there is an error in Section 3. The error: Corollary 3.22 Let ( X , σ b ) $( X,\sigma_{b} ) $ be a complete b-metric-like space with parameter s ≥ 1 $s \ge 1$ , and let f, g be two self-maps of X with ψ ∈ Ψ $\psi \...

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Autores principales: Kastriot Zoto, B. E. Rhoades, Stojan Radenović
Formato: article
Lenguaje:EN
Publicado: SpringerOpen 2018
Materias:
Applied mathematics. Quantitative methods
T57-57.97
Analysis
QA299.6-433
Acceso en línea:https://doaj.org/article/269d846396d44746b9c20d26ed4dad40
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spelling oai:doaj.org-article:269d846396d44746b9c20d26ed4dad402021-12-02T11:03:06ZCorrection to: Some generalizations for ( α − ψ , ϕ ) $(\alpha-\psi,\phi)$ -contractions in b-metric-like spaces and an application10.1186/s13663-018-0629-01687-1812https://doaj.org/article/269d846396d44746b9c20d26ed4dad402018-01-01T00:00:00Zhttp://link.springer.com/article/10.1186/s13663-018-0629-0https://doaj.org/toc/1687-1812Abstract In the publication of this article [Fixed Point Theory Appl. 2017:26, 2017], there is an error in Section 3. The error: Corollary 3.22 Let ( X , σ b ) $( X,\sigma_{b} ) $ be a complete b-metric-like space with parameter s ≥ 1 $s \ge 1$ , and let f, g be two self-maps of X with ψ ∈ Ψ $\psi \in \Psi $ , φ ∈ Φ $\varphi \in \Phi $ satisfying the condition ψ ( α q s p σ b ( f x , f y ) ) ≤ λ ψ ( M ( x , y ) ) $$ \psi \bigl( \alpha_{qs^{p}}\sigma_{b} ( fx,fy ) \bigr) \le \lambda \psi \bigl( M ( x,y ) \bigr) $$ for all x , y ∈ X $x,y \in X$ , where M ( x , y ) $M ( x,y ) $ is defined as in (3.15) and q > 1 $q > 1$ . Then f and g have a unique common fixed point in X. Should instead read: Corollary 3.22 Let ( X , σ b ) $( X,\sigma_{b} ) $ be a complete b-metric-like space with parameter s ≥ 1 $s \ge 1$ , f : X → X $f:X \to X$ be a self-mapping, and α : X × X → [ 0 , ∞ ) $\alpha :X \times X \to \mathopen[ 0,\infty \mathclose) $ . Suppose that the following conditions are satisfied: (i) f is an α q s p $\alpha_{qs^{p}} $ -admissible mapping; (ii) there exists a function ψ ∈ Ψ $\psi \in \Psi $ such that ψ ( α q s p σ b ( f x , f y ) ) ≤ λ ψ ( M ( x , y ) ) ; $$ \psi \bigl( \alpha_{qs^{p}}\sigma_{b} ( fx,fy ) \bigr) \le \lambda \psi \bigl( M ( x,y ) \bigr) ; $$ (iii) there exists x 0 ∈ X $x_{0} \in X$ such that α ( x 0 , f x 0 ) ≥ q s p $\alpha ( x_{0},fx_{0} ) \ge qs^{p}$ ; (iv) either f is continuous or property H q s p $H_{qs^{p}}$ is satisfied. Then f has a fixed point x ∈ X $x \in X$ . Moreover, f has a unique fixed point if property U q s p $U_{qs^{p}}$ is satisfied. This has now been included in this erratum.Kastriot ZotoB. E. RhoadesStojan RadenovićSpringerOpenarticleApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Applications, Vol 2018, Iss 1, Pp 1-2 (2018)
institution DOAJ
collection DOAJ
language EN
topic Applied mathematics. Quantitative methods
T57-57.97
Analysis
QA299.6-433
spellingShingle Applied mathematics. Quantitative methods
T57-57.97
Analysis
QA299.6-433
Kastriot Zoto
B. E. Rhoades
Stojan Radenović
Correction to: Some generalizations for ( α − ψ , ϕ ) $(\alpha-\psi,\phi)$ -contractions in b-metric-like spaces and an application
description Abstract In the publication of this article [Fixed Point Theory Appl. 2017:26, 2017], there is an error in Section 3. The error: Corollary 3.22 Let ( X , σ b ) $( X,\sigma_{b} ) $ be a complete b-metric-like space with parameter s ≥ 1 $s \ge 1$ , and let f, g be two self-maps of X with ψ ∈ Ψ $\psi \in \Psi $ , φ ∈ Φ $\varphi \in \Phi $ satisfying the condition ψ ( α q s p σ b ( f x , f y ) ) ≤ λ ψ ( M ( x , y ) ) $$ \psi \bigl( \alpha_{qs^{p}}\sigma_{b} ( fx,fy ) \bigr) \le \lambda \psi \bigl( M ( x,y ) \bigr) $$ for all x , y ∈ X $x,y \in X$ , where M ( x , y ) $M ( x,y ) $ is defined as in (3.15) and q > 1 $q > 1$ . Then f and g have a unique common fixed point in X. Should instead read: Corollary 3.22 Let ( X , σ b ) $( X,\sigma_{b} ) $ be a complete b-metric-like space with parameter s ≥ 1 $s \ge 1$ , f : X → X $f:X \to X$ be a self-mapping, and α : X × X → [ 0 , ∞ ) $\alpha :X \times X \to \mathopen[ 0,\infty \mathclose) $ . Suppose that the following conditions are satisfied: (i) f is an α q s p $\alpha_{qs^{p}} $ -admissible mapping; (ii) there exists a function ψ ∈ Ψ $\psi \in \Psi $ such that ψ ( α q s p σ b ( f x , f y ) ) ≤ λ ψ ( M ( x , y ) ) ; $$ \psi \bigl( \alpha_{qs^{p}}\sigma_{b} ( fx,fy ) \bigr) \le \lambda \psi \bigl( M ( x,y ) \bigr) ; $$ (iii) there exists x 0 ∈ X $x_{0} \in X$ such that α ( x 0 , f x 0 ) ≥ q s p $\alpha ( x_{0},fx_{0} ) \ge qs^{p}$ ; (iv) either f is continuous or property H q s p $H_{qs^{p}}$ is satisfied. Then f has a fixed point x ∈ X $x \in X$ . Moreover, f has a unique fixed point if property U q s p $U_{qs^{p}}$ is satisfied. This has now been included in this erratum.
format article
author Kastriot Zoto
B. E. Rhoades
Stojan Radenović
author_facet Kastriot Zoto
B. E. Rhoades
Stojan Radenović
author_sort Kastriot Zoto
title Correction to: Some generalizations for ( α − ψ , ϕ ) $(\alpha-\psi,\phi)$ -contractions in b-metric-like spaces and an application
title_short Correction to: Some generalizations for ( α − ψ , ϕ ) $(\alpha-\psi,\phi)$ -contractions in b-metric-like spaces and an application
title_full Correction to: Some generalizations for ( α − ψ , ϕ ) $(\alpha-\psi,\phi)$ -contractions in b-metric-like spaces and an application
title_fullStr Correction to: Some generalizations for ( α − ψ , ϕ ) $(\alpha-\psi,\phi)$ -contractions in b-metric-like spaces and an application
title_full_unstemmed Correction to: Some generalizations for ( α − ψ , ϕ ) $(\alpha-\psi,\phi)$ -contractions in b-metric-like spaces and an application
title_sort correction to: some generalizations for ( α − ψ , ϕ ) $(\alpha-\psi,\phi)$ -contractions in b-metric-like spaces and an application
publisher SpringerOpen
publishDate 2018
url https://doaj.org/article/269d846396d44746b9c20d26ed4dad40
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