### Journals Information

**
Mathematics and Statistics Vol. 9(6), pp. 908 - 916 DOI: 10.13189/ms.2021.090606 Reprint (PDF) (327Kb) **

## Some New Results on Equivalent Cauchy Sequences and Their Applications to Meir-Keeler Contraction in Partial Rectangular Metric Space

**Sidite Duraj ^{1}, Eriola Sila ^{2}^{,*}, Elida Hoxha ^{2}**

^{1}Department of Mathematics, Faculty of Natural Sciences, University of Shkodra, Albania

^{2}Department of Mathematics, Faculty of Natural Sciences, University of Tirana, Albania

**ABSTRACT**

The study of fixed points in the metric spaces plays a crucial role in the development of Functional Analysis. It is evolved by generalizing the metric space or improving the contractive conditions. Recently, the partial rectangular metric space and its topology have been the center of study for many researchers. They have defined open and closed balls the equivalent Cauchy sequences and Cauchy sequences, convergent sequences which are used as tools in many achieved results. In this paper, two facts for equivalent Cauchy sequences in a partial rectangular metric space are provided by using an ultra - altering distance function. Furthermore, some results of Cauchy sequences in a partial rectangular metric space are highlighted. There is proved that under some conditions the equivalent Cauchy sequences are Cauchy sequences in a partial rectangular metric space. Some fixed point results have been taken as applications of our new conditions of Cauchy sequences and equivalent Cauchy sequences in a partial rectangular metric space for orbitally continuous functions . To illustrate the obtained results some examples are given.

**KEYWORDS**

Partial Rectangular Metric Space, Equivalent Cauchy Sequences, Cauchy Sequences, Fixed Point

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Sidite Duraj , Eriola Sila , Elida Hoxha , "Some New Results on Equivalent Cauchy Sequences and Their Applications to Meir-Keeler Contraction in Partial Rectangular Metric Space," Mathematics and Statistics, Vol. 9, No. 6, pp. 908 - 916, 2021. DOI: 10.13189/ms.2021.090606.

(b). APA Format:

Sidite Duraj , Eriola Sila , Elida Hoxha (2021). Some New Results on Equivalent Cauchy Sequences and Their Applications to Meir-Keeler Contraction in Partial Rectangular Metric Space. Mathematics and Statistics, 9(6), 908 - 916. DOI: 10.13189/ms.2021.090606.