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

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:

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

• (ii) there exists a function $\psi \in \Psi$ such that

  $$ \psi \bigl( \alpha_{qs^{p}}\sigma_{b} ( fx,fy ) \bigr) \le \lambda \psi \bigl( M ( x,y ) \bigr) ; $$

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

• (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.