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

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

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.

References

  1. 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

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Correspondence to Kastriot Zoto.

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The online version of the original article can be found under https://doi.org/10.1186/s13663-017-0620-1.

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Zoto, K., Rhoades, B.E. & Radenović, S. Correction to: Some generalizations for \((\alpha-\psi,\phi)\)-contractions in b-metric-like spaces and an application. Fixed Point Theory Appl 2018, 4 (2018) doi:10.1186/s13663-018-0629-0

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