Some best proximity point results on best orbitally complete quasi metric spaces

Mustafa Aslantas; Hakan Sahin; Raghad Jabbar Sabir Al-Okbi; Mustafa Aslantas; Hakan Sahin; Raghad Jabbar Sabir Al-Okbi

doi:10.3934/math.2023401

AIMS Mathematics

2023, Volume 8, Issue 4: 7967-7980. doi: 10.3934/math.2023401

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Research article

Some best proximity point results on best orbitally complete quasi metric spaces

1.
Department of Mathematics, Faculty of Science, Çankırı Karatekin University, Çankırı 18100, Turkey
2.
Department of Mathematics, Faculty of Engineering and Natural Sciences, Bursa Technical University, Bursa 16310, Turkey

Received: 17 November 2022 Revised: 13 January 2023 Accepted: 18 January 2023 Published: 31 January 2023
MSC : 54H25, 47H10

In this paper, we first introduce the concepts of $ d $- and $ d^{-1} $-proximal Ćirić contraction mappings. Also, we present new definitions and notations by taking into account the lack of symmetry property of quasi-metric spaces. Moreover, we give some examples to support our definitions and notations. Then, we prove some right and left best proximity point results for these mappings on best orbitally complete quasi-metric spaces. Hence, we obtain some generalizations of famous results in the literature.
- best proximity point,
- orbitally continuous mapping,
- quasi-metric space
Citation: Mustafa Aslantas, Hakan Sahin, Raghad Jabbar Sabir Al-Okbi. Some best proximity point results on best orbitally complete quasi metric spaces[J]. AIMS Mathematics, 2023, 8(4): 7967-7980. doi: 10.3934/math.2023401

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Abstract

In this paper, we first introduce the concepts of $ d $- and $ d^{-1} $-proximal Ćirić contraction mappings. Also, we present new definitions and notations by taking into account the lack of symmetry property of quasi-metric spaces. Moreover, we give some examples to support our definitions and notations. Then, we prove some right and left best proximity point results for these mappings on best orbitally complete quasi-metric spaces. Hence, we obtain some generalizations of famous results in the literature.

References

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