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: | , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
SpringerOpen
2018
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/269d846396d44746b9c20d26ed4dad40 |
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| Sumario: | 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. |
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