An inevitable note on bipolar metric spaces

Erdal Karapınar; Marija Cvetković; Erdal Karapınar; Marija Cvetković

doi:10.3934/math.2024162

AIMS Mathematics

2024, Volume 9, Issue 2: 3320-3331. doi: 10.3934/math.2024162

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An inevitable note on bipolar metric spaces

Erdal Karapınar ^1,2,
Marija Cvetković ^{3
,
,}

1.
Department of Mathematics, Çankaya University, Etimesgut, Ankara, Turkey
2.
Department of Medical Research, China Medical University Hospital, China Medical University, 40402 Taichung, Taiwan
3.
Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia

Received: 20 November 2023 Revised: 19 December 2023 Accepted: 26 December 2023 Published: 04 January 2024
MSC : 47H10, 54H25

Bipolar metric spaces and related fixed point theorems therein were introduced based on the motivation of measuring the distance between the elements of distinct sets. The question regarding the independence of these results from the analogous results on a fixed point of an induced mapping on a Cartesian product of two sets. We proved that bipolar metric space is metrizable and we presented two different approaches for defining a metric induced by a bipolar metric. Two obtained metric spaces demonstrated the lack of novelty of fixed point theorems for covariant and contravariant contraction.
- metric,
- bipolar metric,
- Banach contraction,
- Kannan contraction
Citation: Erdal Karapınar, Marija Cvetković. An inevitable note on bipolar metric spaces[J]. AIMS Mathematics, 2024, 9(2): 3320-3331. doi: 10.3934/math.2024162

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Abstract

Bipolar metric spaces and related fixed point theorems therein were introduced based on the motivation of measuring the distance between the elements of distinct sets. The question regarding the independence of these results from the analogous results on a fixed point of an induced mapping on a Cartesian product of two sets. We proved that bipolar metric space is metrizable and we presented two different approaches for defining a metric induced by a bipolar metric. Two obtained metric spaces demonstrated the lack of novelty of fixed point theorems for covariant and contravariant contraction.

References

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