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  • Correction
  • Open Access

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

Fixed Point Theory and Applications20182018:4

https://doi.org/10.1186/s13663-018-0629-0

  • Received: 23 December 2017
  • Accepted: 23 December 2017
  • Published:

The original article was published in Fixed Point Theory and Applications 2017 2017:26

1 Correction

In the publication of this article [1], there is an error in Section 3.

The error:

Corollary 3.22

Let \(( X,\sigma_{b} ) \) be a complete b-metric-like space with parameter \(s \ge 1\), and let f, g be two self-maps of X with \(\psi \in \Psi \), \(\varphi \in \Phi \) satisfying the condition
$$ \psi \bigl( \alpha_{qs^{p}}\sigma_{b} ( fx,fy ) \bigr) \le \lambda \psi \bigl( M ( x,y ) \bigr) $$
for all \(x,y \in X\), where \(M ( x,y ) \) is defined as in (3.15) and \(q > 1\). Then f and g have a unique common fixed point in X.

Should instead read:

Corollary 3.22

Let \(( X,\sigma_{b} ) \) be a complete b-metric-like space with parameter \(s \ge 1\), \(f:X \to X\) be a self-mapping, and \(\alpha :X \times X \to \mathopen[ 0,\infty \mathclose) \). Suppose that the following conditions are satisfied:
  1. (i)

    f is an \(\alpha_{qs^{p}} \)-admissible mapping;

     
  2. (ii)
    there exists a function \(\psi \in \Psi \) such that
    $$ \psi \bigl( \alpha_{qs^{p}}\sigma_{b} ( fx,fy ) \bigr) \le \lambda \psi \bigl( M ( x,y ) \bigr) ; $$
     
  3. (iii)

    there exists \(x_{0} \in X\) such that \(\alpha ( x_{0},fx_{0} ) \ge qs^{p}\);

     
  4. (iv)

    either f is continuous or property \(H_{qs^{p}}\) is satisfied.

     
Then f has a fixed point \(x \in X\). Moreover, f has a unique fixed point if property \(U_{qs^{p}}\) is satisfied.

The error:

Corollary 3.17

(ii) there exist functions \(\psi,\varphi \in \Psi\) such that
$$\psi \bigl( \alpha ( x,y )\sigma_{b}(fx,fy) \bigr) \le \beta \bigl( N(x,y) \bigr)N(x,y); $$

Should instead read:

Corollary 3.17

(ii) there exists function \(\beta \in \mathbb{S}\) such that
$$\alpha ( x,y )\sigma_{b}(fx,fy) \le \beta \bigl( N(x,y)\bigr)N(x,y); $$

This has now been included in this erratum.

Notes

Declarations

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors’ Affiliations

(1)
Department of Mathematics and Computer Sciences, Faculty of Natural Sciences, University of Gjirokastra, Gjirokastra, Albania
(2)
Department of Mathematics, Indiana University, Bloomington, USA
(3)
Faculty of Mechanical Engineering, University of Belgrade, Beograd, Serbia
(4)
State University of Novi Pazar, Novi Pazar, Serbia

References

  1. Zoto, K, Rhoades, BE, Radenović, S: Some generalizations for \((\alpha-\psi,\phi)\)-contractions in b-metric-like spaces and an application. Fixed Point Theory Appl. 2017, 26 (2017). https://doi.org/10.1186/s13663-017-0620-1 MathSciNetView ArticleGoogle Scholar

Copyright

© The Author(s) 2018

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