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We consider some Nemytzki-Edelstein-Meir-Keeler type results in the context of b-metric spaces. In some cases, we assume that the b-metric is continuous. Our results generalize several known ones in existing literature. We also present some examples to illustrate the usability of our results.

Let

Let

For other fixed point results via generalized Meir-Keeler contractions, see [

Let

The following example shows that Ćirić result is a proper generalization of Meir-Keeler theorem.

Let

Theorems

On the other hand, Bakhtin [

Let

The triplet

In the last period, many authors obtained several fixed point results for single-valued or set-valued mappings in the context of

Let

The concepts of

The following two lemmas are very significant in the class of

Let

Let

Since in general a b-metric is not continuous, we need the following two lemmas.

Let

Let

Essential to the proofs of fixed point theorems for the most contractive conditions in the context of b-metric spaces are the above two lemmas (see, for example, [

To our knowledge, it is not known whether Meir-Keeler and Ćirić theorems hold in the context of

Our first result generalizes Lemma 1 of [

Let

Since

If condition (

However, with a stronger condition than (

Now, we announce a Meir-Keeler type result in the context of b-metric spaces.

Let

Given

Then

It is clear that, for all

Let

Let

(

(

(

Therefore, condition (

Now, we give an example supporting Theorem

Let

Let

The following is Geraghty type result in the context of

Let

Since

It is well known that, in compact metric spaces, fixed point results can be obtained under the strict contractive condition (

Let

Define a function

Let

Consider the real sequence

The two previous theorems are known in literature as Nemytzki and Edelstein theorems, respectively. It is clear that Edelstein theorem extends the result of Nemytzki.

In the sequel, we consider

A mapping

Let

Since

Now, consider a class of mappings

For every

It is obvious that any contractive mapping is eventually contractive (it satisfies (

Contractive and

Now, we announce the next result.

Let

If

Assume now that

Now, we show that

If

A mapping

Let

The proof is very similar to the ones in the previous theorem. Therefore, it is omitted.

If

The following two results extend ones from standard metric spaces to b-metric spaces (see [

Let

Define

Let

Let

No data is used to support this study.

The authors declare that they have no conflicts of interest regarding the publication of this paper.