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We admonish to be careful on studying coupled fixed point theorems since most of the reported fixed point results can be easily derived from the existing corresponding theorems in the literature. In particular, we notice that the recent paper [Semwal and Dimri (2014)] has gaps and the announced result is false. The authors claimed that their result generalized the main result in [Ðoric and Lazović (2011)] but, in fact, the contrary case is true. Finally, we present a fixed point theorem for Suzuki type (

Throughout this note, we follow the notions and notations given in [

Very recently, Semwal and Dimri [

Let

Semwal and Dimri [

Let

This note is devoted to the following three aims.

Let us review the lines of their proof. First at all, notice that, in general, if

The authors took

Furthermore, assume that we would have been able to apply the mentioned contractivity condition. In this case, the authors wrote the following (see [

The same mistake occurred when the authors tried to upper bound the terms

If we want to modify the contractivity condition given in Theorem

Let

However, we claim that this result is not a proper generalization of Theorem

Given a metric

Notice that

Given a mapping

Notice that antecedent condition (

Theorem

It is evident from (

In this section, we introduce a generalization of Theorem

Let

We say that the metric space

If

Let

In the following theorem, we will use the following condition, which can be verified for

We must clarify that this condition is always satisfied when

If

Since

Let

there exist

at least, one of the following properties holds:

Then

Taking into account Remark

We follow the lines of the proof of Theorem 1.2 in [

In this case, using that

Next, we are going to show the following claim:

Next we distinguish between the cases

Given

Two cases can be considered. If

On the contrary, assume that

In any case, using (

If we take

Theorem

In the next example we show that Theorem

Let

Indeed, let

The authors declare that they have no competing interests regarding the publication of this paper.

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

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, under Grant no. 55-130-35-HiCi. The authors, therefore, acknowledge technical and financial support of KAU. The fourth author has been partially supported by Junta de Andaluca by Project FQM-268 of the Andalusian CICYE.