Research Article
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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

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.

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

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.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Kübra ÖZKAN (Primary Author)
MANISA CELAL BAYAR UNIVERSITY
0000-0002-8014-1713
Türkiye


Utku GÜRDAL
MEHMET AKIF ERSOY UNIVERSITY
Türkiye

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

Cite

Bibtex @research article { konuralpjournalmath609766, journal = {Konuralp Journal of Mathematics}, issn = {}, eissn = {2147-625X}, address = {}, publisher = {Mehmet Zeki SARIKAYA}, year = {2020}, volume = {8}, pages = {137 - 143}, doi = {}, title = {The Fixed Point Theorem and Characterization of Bipolar Metric Completeness}, key = {cite}, author = {Özkan, Kübra and Gürdal, Utku} }
APA Özkan, K. & Gürdal, U. (2020). The Fixed Point Theorem and Characterization of Bipolar Metric Completeness . Konuralp Journal of Mathematics , 8 (1) , 137-143 . Retrieved from https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/31494/609766
MLA Özkan, K. , Gürdal, U. "The Fixed Point Theorem and Characterization of Bipolar Metric Completeness" . Konuralp Journal of Mathematics 8 (2020 ): 137-143 <https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/31494/609766>
Chicago Özkan, K. , Gürdal, U. "The Fixed Point Theorem and Characterization of Bipolar Metric Completeness". Konuralp Journal of Mathematics 8 (2020 ): 137-143
RIS TY - JOUR T1 - The Fixed Point Theorem and Characterization of Bipolar Metric Completeness AU - Kübra Özkan , Utku Gürdal Y1 - 2020 PY - 2020 N1 - DO - T2 - Konuralp Journal of Mathematics JF - Journal JO - JOR SP - 137 EP - 143 VL - 8 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2020 ER -
EndNote %0 Konuralp Journal of Mathematics The Fixed Point Theorem and Characterization of Bipolar Metric Completeness %A Kübra Özkan , Utku Gürdal %T The Fixed Point Theorem and Characterization of Bipolar Metric Completeness %D 2020 %J Konuralp Journal of Mathematics %P -2147-625X %V 8 %N 1 %R %U
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 .
AMA Özkan K. , Gürdal U. The Fixed Point Theorem and Characterization of Bipolar Metric Completeness. Konuralp J. Math.. 2020; 8(1): 137-143.
Vancouver Özkan K. , Gürdal U. The Fixed Point Theorem and Characterization of Bipolar Metric Completeness. Konuralp Journal of Mathematics. 2020; 8(1): 137-143.
IEEE K. Özkan and U. Gürdal , "The Fixed Point Theorem and Characterization of Bipolar Metric Completeness", Konuralp Journal of Mathematics, vol. 8, no. 1, pp. 137-143, Apr. 2020
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