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The Fixed Point Theorem and Characterization of Bipolar Metric Completeness

Year 2020, Volume: 8 Issue: 1, 137 - 143, 15.04.2020

Kübra Özkan Utku Gürdal

Abstract

In this article, we prove a fixed point theorem, which is generalization of Banach fixed point theorem and characterizes the metric completeness, for contravariant mapping on bipolar metric spaces. And, we give some results related to this fixed point theorem.

Keywords

bipolar metric space completeness fixed point theory

References

  • [1] M. Abbas, B. Ali and C. Vetro, A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces, Topology and Its Applications, Vol:160, No.3, (2013), 553–563.
  • [2] M. Abbas, H. Iqbal and A. Petrusel, Fixed points for multivalued Suzuki type (q;R)-contraction mapping with applications, Journal of Function Spaces, Vol: 2019, Article ID 9565804, 13 pages, 2019. https://doi.org/10.1155/2019/9565804.
  • [3] N. Chandraa, M.C. Aryaa and Mahesh C. Joshia, A Suzuki-Type Common Fixed Point Theorem, Filomat, Vol:31, No.10 (2017), 2951–2956.
  • [4] L. Ciric, M. Abbas, M. Rajovic´ and B. Ali, Suzuki type fixed point theorems for generalized multi-valued mappings on a set endowed with two b-metrics, Applied Mathematics and Computation, Vol:219, No.4 (2012), 1712-1723.
  • [5] D. Doric, Z. Kadelburg and S. Radenovic, Edelstein-Suzuki-type fixed point results in metric spaces, Nonlinear Analysis: Theory, Methods and Applications, Vol:75, (2012), 1927–1932.
  • [6] A. Mutlu and U. Gurdal, Bipolar metric spaces and some fixed point theorems, Journal of Nonlinear Sciences and Applications, Vol:9, No.9 (2016), 5362–5373.
  • [7] A. Mutlu, K. Ozkan and U. Gurdal, Coupled Fixed Point Theorems on Bipolar Metric Spaces, European Journal of Pure and Applied Mathematics, Vol:10, No.4 (2017), 655–667.
  • [8] A. Mutlu, K. Ozkan and U. Gu¨rdal, Fixed point theorems for multivalued mappings on bipolar metric spaces, Fixed Point Theory, Vol: 21, No.1, (2020), 271–280.
  • [9] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society, Vol:136, (2008), 1861-1869.
  • [10] T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Analysis: Theory, Methods and Applications, Vol:71, No.11 (2009), 5313–5317.
  • [11] D. Paesano and P. Vetro, Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology and Its Applications, Vol:159, No.3 (2012), 911–920.

Year 2020, Volume: 8 Issue: 1, 137 - 143, 15.04.2020

Kübra Özkan Utku Gürdal

Abstract

References

  • [1] M. Abbas, B. Ali and C. Vetro, A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces, Topology and Its Applications, Vol:160, No.3, (2013), 553–563.
  • [2] M. Abbas, H. Iqbal and A. Petrusel, Fixed points for multivalued Suzuki type (q;R)-contraction mapping with applications, Journal of Function Spaces, Vol: 2019, Article ID 9565804, 13 pages, 2019. https://doi.org/10.1155/2019/9565804.
  • [3] N. Chandraa, M.C. Aryaa and Mahesh C. Joshia, A Suzuki-Type Common Fixed Point Theorem, Filomat, Vol:31, No.10 (2017), 2951–2956.
  • [4] L. Ciric, M. Abbas, M. Rajovic´ and B. Ali, Suzuki type fixed point theorems for generalized multi-valued mappings on a set endowed with two b-metrics, Applied Mathematics and Computation, Vol:219, No.4 (2012), 1712-1723.
  • [5] D. Doric, Z. Kadelburg and S. Radenovic, Edelstein-Suzuki-type fixed point results in metric spaces, Nonlinear Analysis: Theory, Methods and Applications, Vol:75, (2012), 1927–1932.
  • [6] A. Mutlu and U. Gurdal, Bipolar metric spaces and some fixed point theorems, Journal of Nonlinear Sciences and Applications, Vol:9, No.9 (2016), 5362–5373.
  • [7] A. Mutlu, K. Ozkan and U. Gurdal, Coupled Fixed Point Theorems on Bipolar Metric Spaces, European Journal of Pure and Applied Mathematics, Vol:10, No.4 (2017), 655–667.
  • [8] A. Mutlu, K. Ozkan and U. Gu¨rdal, Fixed point theorems for multivalued mappings on bipolar metric spaces, Fixed Point Theory, Vol: 21, No.1, (2020), 271–280.
  • [9] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society, Vol:136, (2008), 1861-1869.
  • [10] T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Analysis: Theory, Methods and Applications, Vol:71, No.11 (2009), 5313–5317.
  • [11] D. Paesano and P. Vetro, Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology and Its Applications, Vol:159, No.3 (2012), 911–920.
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Kübra Özkan

Utku Gürdal

Publication Date April 15, 2020
Submission Date August 23, 2019
Acceptance Date April 2, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Özkan, K., & Gürdal, U. (2020). The Fixed Point Theorem and Characterization of Bipolar Metric Completeness. Konuralp Journal of Mathematics, 8(1), 137-143.
AMA Özkan K, Gürdal U. The Fixed Point Theorem and Characterization of Bipolar Metric Completeness. Konuralp J. Math. April 2020;8(1):137-143.
Chicago Özkan, Kübra, and Utku Gürdal. “The Fixed Point Theorem and Characterization of Bipolar Metric Completeness”. Konuralp Journal of Mathematics 8, no. 1 (April 2020): 137-43.
EndNote Özkan K, Gürdal U (April 1, 2020) The Fixed Point Theorem and Characterization of Bipolar Metric Completeness. Konuralp Journal of Mathematics 8 1 137–143.
IEEE K. Özkan and U. Gürdal, “The Fixed Point Theorem and Characterization of Bipolar Metric Completeness”, Konuralp J. Math., vol. 8, no. 1, pp. 137–143, 2020.
ISNAD Özkan, Kübra - Gürdal, Utku. “The Fixed Point Theorem and Characterization of Bipolar Metric Completeness”. Konuralp Journal of Mathematics 8/1 (April 2020), 137-143.
JAMA Özkan K, Gürdal U. The Fixed Point Theorem and Characterization of Bipolar Metric Completeness. Konuralp J. Math. 2020;8:137–143.
MLA Özkan, Kübra and Utku Gürdal. “The Fixed Point Theorem and Characterization of Bipolar Metric Completeness”. Konuralp Journal of Mathematics, vol. 8, no. 1, 2020, pp. 137-43.
Vancouver Özkan K, Gürdal U. The Fixed Point Theorem and Characterization of Bipolar Metric Completeness. Konuralp J. Math. 2020;8(1):137-43.
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