Double controlled quasi metric-like spaces and some topological properties of this space

A. M. Zidan; Z. Mostefaoui; A. M. Zidan; Z. Mostefaoui

doi:10.3934/math.2021672

AIMS Mathematics

2021, Volume 6, Issue 10: 11584-11594. doi: 10.3934/math.2021672

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Research article

Double controlled quasi metric-like spaces and some topological properties of this space

A. M. Zidan ^{1,2
,
,},
Z. Mostefaoui ³

1.
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch 71524, Egypt
3.
Department of Mathematics, E.N.S, B.P. 92 Vieux Kouba 16050 Algiers, Algeria

Received: 05 April 2021 Accepted: 04 August 2021 Published: 10 August 2021
MSC : 30L10, 37C25, 46A19

In present paper, we introduce a new extension of the double controlled metric-like spaces, so called double controlled quasi metric-like spaces "assuming that the self-distance may not be zero". Also, if the value of the metric is zero, then it has to be "a self-distance". After that, by using this new type of quasi metric spaces, we generalize many results in the literature and we prove fixed point theorems along with some examples illustrating.
- uasi metric-like spaces,
- double controlled,
- fixed point theory
Citation: A. M. Zidan, Z. Mostefaoui. Double controlled quasi metric-like spaces and some topological properties of this space[J]. AIMS Mathematics, 2021, 6(10): 11584-11594. doi: 10.3934/math.2021672

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Abstract

In present paper, we introduce a new extension of the double controlled metric-like spaces, so called double controlled quasi metric-like spaces "assuming that the self-distance may not be zero". Also, if the value of the metric is zero, then it has to be "a self-distance". After that, by using this new type of quasi metric spaces, we generalize many results in the literature and we prove fixed point theorems along with some examples illustrating.

References

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