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We show that the main result in the work by Mutlu et al. is not true. We explain point by point some of its main mistakes and we propose an alternative version to smooth away the defects of it.

Following Matthews [

In [

Assume that

Suppose that

In this paper, we show that Definition

To better understand our main claims, let us introduce the following definitions and notation. In the sequel,

A

In [

Let

Given two mappings

Henceforth, we will use the notation

In the following lines, we must do the following commentaries in order to advise researchers about proving new results based on Theorem

First of all, we point out that Definition

Therefore,

As a consequence, Theorem

Although Theorem

The authors did not clarify if

The previous remark is important because if we take

which, in the metric case, let bound the distance

In [

However, it is not clear why

With respect to the previous remark, it is also necessary to point out that the contractivity condition (

Let us see where the mistake is. Theorem

occurs provided that

then

In this case, it was not proved that

Similarly, the contractivity condition (

but, in this case, the inequalities

When the authors tried to prove that the sequences

and if

(see [

Other important mistakes can be found in [

Taking into account that

Finally, we point out that Theorem 7 in [

It is not clear how we can show a counterexample of Theorem

Let

Let

Taking into account the commentaries given in Section

In recent times, many coupled/tripled/quadrupled/multidimensional fixed point theorems in various abstract metric spaces have come to be simple consequences of their corresponding unidimensional results (see, e.g., [

Let

Two points

A subset

A mapping

One will say that

Let

Very recently, Nashine et al. [

Let

Then, the set

Based on this result, we present a coupled version that can be interpreted as a correct version of Mutlu et al.’s theorem.

Let

To prove it, we use the following notation and basic facts. Let

Given two mappings

We first note that we can suggest further corrected forms for the paper [

Secondly, we can list several consequences of Theorem

Finally, independently from the structure of the abstract space (e.g., metric space, partial metric space,

The authors declare that they have no competing interests.

All authors contributed equally and significantly in writing this paper. All authors read and approved the final paper.

This research was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia. The authors thank the anonymous referees for their remarkable comments, suggestions, and ideas that helped to improve this paper. Antonio Francisco Roldán Lόpez de Hierro has been partially supported by Junta de Andalucía by project FQM-268 of the Andalusian CICYE.

^{*}-metric spaces