Research Article
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Year 2024, Volume: 6 Issue: 1, 29 - 43, 30.06.2024
https://doi.org/10.47086/pims.1442731

Abstract

References

  • M. Aslantas, H. Sahin and D. Turkoglu, Some Caristi type fixed point theorems, The Journal of Analysis, 29 (2021), 89—103. https://doi.org/10.1007/s41478-020-00248-8
  • M. Aslantas, H. Sahin and U. Sadullah, Some generalizations for mixed multivalued mappings, Appl. Gen. Topol., 23(1) (2022), 169–178. https://doi.org/10.4995/agt.2022.15214
  • I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Functional Analysis, 30 (1989), 26–37.
  • S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales. Fundamenta Mathematicae., 3 (1922), 133–181.
  • V. Berinde, Generalized contractions in quasi metric spaces, Seminar on Fixed Point Theory, 3 (1993), 3–9. Preprint
  • S. Czerwik, Contraction mappings in b−metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis, 1 (1993), 5-11.
  • S. Cetin and U. Gürdal, Characterization of bipolar ultrametric spaces and some fixed point theorems, Hacettepe Journal of Mathematics and Statistics, 52(1) (2023), 185 -– 196. DOI : 10.15672/hujms.1024696
  • U. Gürdal, A. Mutlu and K. Özkan, Fixed point results for α − ψ−contractive mappings in bipolar metric spaces, Journal of Inequalities and Special Functions, 11(1) (2020), 64–75.
  • T. Kamran, M. Samreen and Q. UL Ain, A generalization of b−metric space and some fixed point theorems, Mathematics, 5(2) (2017), 1–7.
  • A. Mutlu A. and U. Gürdal, Bipolar metric spaces and some fixed point theorems, Journal of Nonlinear Sciences and Applications, 9(9) (2016), 5362–5373.
  • A. Mutlu, K. Özkan and U. Gürdal, Coupled fixed point theorems on bipolar metric spaces. European Journal of Pure And Applied Mathematics, 10(4) (2017), 655–667.
  • A. Mutlu, K. Özkan and U. Gürdal, C, Locally and weakly contractive principle in bipolar metric spaces. TurkishWorld Mathematical Society Journal of Applied and Engineering Mathematics, 10(2) (2020), 379– 388.
  • A. Mutlu, K. Özkan and U. Gürdal, C, Fixed point theorems for multivalued mappings on bipolar metric spaces, Fixed Point Theory, 21(1) (2020), 271–280. doi: 10.24193/fpt-ro.2020.1.19 BIPOLAR b−METRIC SPACES 43
  • K. Özkan, U. Gürdal and A. Mutlu, Generalization of Amini-Harandi’s fixed point theorem with an application to nonlinear mapping theory. Fixed Point Theory, 21(2) (2020), 707–714. doi: 10.24193/fptro. 2020.2.50
  • K. Özkan, U. Gürdal and A. Mutlu Caristi’s and Downing-Kirk’s fixed point theorems on bipolar metric spaces. Fixed Point Theory, 21(2) (2021), 785–794. doi: 10.24193/fpt-ro.2021.2.51
  • A. Mutlu, K. Özkan and U. Gürdal, Some Common Fixed Point Theorems in BipolarMetric Spaces. Turkish Journal of Mathematics and Computer Science, 14(2) (2022), 346–354. doi: 10.47000/tjmcs.1099118
  • H. Sahin, M. Aslantas and A. A. Nasir Nasir, Some Extended Results for Multivalued F-Contraction Mappings, Axioms, 12(2) (2023), 116. https://doi.org/10.3390/axioms12020116

Fixed Point Theorems for Contravariant Maps in Bipolar b-Metric Spaces with Integration Application

Year 2024, Volume: 6 Issue: 1, 29 - 43, 30.06.2024
https://doi.org/10.47086/pims.1442731

Abstract

As a natural extension of the metric and the bipolar metric, this article introduces the new abstract bipolar $b-$
metric. The bipolar $b-$metric is a novel technique addressed in this article; it is explained by combining the
well-known $b-$metric in the theory of metric spaces, as defined by Mutlu and G\"{u}rdal (2016) \cite{mg1}, with the
description of the bipolar metric. In this new definition, well-known mathematical terms such as Cauchy and
convergent sequences are utilized. In the bipolar $b-$metric, fundamental topological concepts are also defined to investigate the existence of fixed points implicated in such mappings under different contraction
conditions. An example is provided to demonstrate the presented results.

Ethical Statement

All authors contributed equally and significantly in writing this article. All authors read and approved the manuscript. The authors declare that they have no conflict of interest. This article does not contain any studies with human participants or animals performed by any of the authors.

Supporting Institution

This research received no external funding.

Thanks

No

References

  • M. Aslantas, H. Sahin and D. Turkoglu, Some Caristi type fixed point theorems, The Journal of Analysis, 29 (2021), 89—103. https://doi.org/10.1007/s41478-020-00248-8
  • M. Aslantas, H. Sahin and U. Sadullah, Some generalizations for mixed multivalued mappings, Appl. Gen. Topol., 23(1) (2022), 169–178. https://doi.org/10.4995/agt.2022.15214
  • I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Functional Analysis, 30 (1989), 26–37.
  • S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales. Fundamenta Mathematicae., 3 (1922), 133–181.
  • V. Berinde, Generalized contractions in quasi metric spaces, Seminar on Fixed Point Theory, 3 (1993), 3–9. Preprint
  • S. Czerwik, Contraction mappings in b−metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis, 1 (1993), 5-11.
  • S. Cetin and U. Gürdal, Characterization of bipolar ultrametric spaces and some fixed point theorems, Hacettepe Journal of Mathematics and Statistics, 52(1) (2023), 185 -– 196. DOI : 10.15672/hujms.1024696
  • U. Gürdal, A. Mutlu and K. Özkan, Fixed point results for α − ψ−contractive mappings in bipolar metric spaces, Journal of Inequalities and Special Functions, 11(1) (2020), 64–75.
  • T. Kamran, M. Samreen and Q. UL Ain, A generalization of b−metric space and some fixed point theorems, Mathematics, 5(2) (2017), 1–7.
  • A. Mutlu A. and U. Gürdal, Bipolar metric spaces and some fixed point theorems, Journal of Nonlinear Sciences and Applications, 9(9) (2016), 5362–5373.
  • A. Mutlu, K. Özkan and U. Gürdal, Coupled fixed point theorems on bipolar metric spaces. European Journal of Pure And Applied Mathematics, 10(4) (2017), 655–667.
  • A. Mutlu, K. Özkan and U. Gürdal, C, Locally and weakly contractive principle in bipolar metric spaces. TurkishWorld Mathematical Society Journal of Applied and Engineering Mathematics, 10(2) (2020), 379– 388.
  • A. Mutlu, K. Özkan and U. Gürdal, C, Fixed point theorems for multivalued mappings on bipolar metric spaces, Fixed Point Theory, 21(1) (2020), 271–280. doi: 10.24193/fpt-ro.2020.1.19 BIPOLAR b−METRIC SPACES 43
  • K. Özkan, U. Gürdal and A. Mutlu, Generalization of Amini-Harandi’s fixed point theorem with an application to nonlinear mapping theory. Fixed Point Theory, 21(2) (2020), 707–714. doi: 10.24193/fptro. 2020.2.50
  • K. Özkan, U. Gürdal and A. Mutlu Caristi’s and Downing-Kirk’s fixed point theorems on bipolar metric spaces. Fixed Point Theory, 21(2) (2021), 785–794. doi: 10.24193/fpt-ro.2021.2.51
  • A. Mutlu, K. Özkan and U. Gürdal, Some Common Fixed Point Theorems in BipolarMetric Spaces. Turkish Journal of Mathematics and Computer Science, 14(2) (2022), 346–354. doi: 10.47000/tjmcs.1099118
  • H. Sahin, M. Aslantas and A. A. Nasir Nasir, Some Extended Results for Multivalued F-Contraction Mappings, Axioms, 12(2) (2023), 116. https://doi.org/10.3390/axioms12020116
There are 17 citations in total.

Details

Primary Language English
Subjects Dynamical Systems in Applications
Journal Section Articles
Authors

Shaban Sedghi 0000-0003-0717-9229

Merryam Sımkha This is me

Utku Gürdal 0000-0003-2887-2188

Ali Mutlu 0000-0003-0008-2432

Early Pub Date July 1, 2024
Publication Date June 30, 2024
Submission Date February 25, 2024
Acceptance Date June 29, 2024
Published in Issue Year 2024 Volume: 6 Issue: 1

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