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

The Original Article was published on 06 December 2017

## Correction

In the publication of this article , 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.

### 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

$$\psi \bigl( \alpha ( x,y )\sigma_{b}(fx,fy) \bigr) \le \beta \bigl( N(x,y) \bigr)N(x,y);$$

### 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. 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

## Author information

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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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