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Year 2023, Volume: 52 Issue: 1, 185 - 196, 15.02.2023

Selim Çetin Utku Gürdal

https://doi.org/10.15672/hujms.1024696
Cited By: 1

Abstract

Keywords

ultrametric space fixed point theorem bipolar metric space

References

  • [1] C. Alaca, M.E. Ege and C. Park, Fixed point results for modular ultrametric spaces, J. Comput. Anal. Appl. 20 (7), 1259–1267, 2016.
  • [2] P. Alexandroff, Zur Begründung der n-dimensionalen mengentheoretischen Topologie, Math. Ann. 94 (1), 296–308, 1925.
  • [3] M. Aschbacher, P. Baldi, E.B. Baum and R.M. Wilson, Embeddings of ultrametric spaces in finite dimensional structures, SIAM J. Algebraic Discrete Methods 8 (4), 564–577, 1987.
  • [4] U. Gürdal, Çift kutuplu metrik uzaylar ve sabit nokta teoremleri (PhD Thesis), Manisa Celâl Bayar Üniversitesi Fen Bilimleri Enstitüsü, Manisa, Türkiye, 2018.
  • [5] U. Gürdal, A. Mutlu and K. Özkan, Fixed point results for $\alpha\psi$-contractive mappings in bipolar metric spaces, J. Inequal. Spec. Funct. 11 (1), 64–75, 2020.
  • [6] J.E. Holy, Pictures of ultrametric spaces, the p-adic numbers, and valued fields, The American Mathematical Monthly 108 (8), 721–728, 2001.
  • [7] L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2), 1468–1476, 2007.
  • [8] B. Hughes, Trees and ultrametric spaces: a categorical equivalence, Adv. Math. 189 (1), 148–191, 2004.
  • [9] F. Murtagh, On ultrametricity, data coding, and computation, J. Classification 21 (2), 167–184, 2004.
  • [10] P.P. Murthy, Z. Mitrović, C.P. Dhuri and S. Radenović, The common fixed points in a bipolar metric space, Gulf J. Math. 12 (2), 31–38, 2022.
  • [11] A. Mutlu and U. Gürdal, Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl. 9 (9), 5362–5373, 2016.
  • [12] A. Mutlu, U. Gürdal and K. Özkan, Fixed point theorems for multivalued mappings on bipolar metric spaces, Fixed Point Theory 21 (1), 271–280, 2020.
  • [13] A. Mutlu, U. Gürdal and K. Özkan, Coupled fixed point theorems on bipolar metric spaces, Eur. J. Pure Appl. Math. 10 (4), 655–667, 2017.
  • [14] A. Mutlu, K. Özkan and U. Gürdal, Locally and weakly contractive principle in bipolar metric spaces, TWMS J. Appl. Eng. Math. 10 (2), 379–388, 2020.
  • [15] A.T. Ogielski and D.L. Stein, Dynamics on ultrametric spaces, Phys. Rev. Lett. 55 (15), 1634, 1985.
  • [16] K. Özkan and U. Gürdal, The fixed point theorem and characterization of bipolar metric completeness, Konuralp J. Math. 8 (1), 137–143, 2020.
  • [17] K. Özkan, U. Gürdal and A. Mutlu, Caristi’s and Downing-Kirk’s fixed point theorems on bipolar metric spaces, Fixed Point Theory, 22 (2), 785–794, 2021.
  • [18] 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), 707–714, 2020.
  • [19] R. Rammal, G. Toulouse and M.A. Virasoro, Ultrametricity for physicists, Rev. Modern Phys. 58 (3), 765, 1986.
  • [20] K. Roy, M. Saha, R. George, L. Guran and Z.D. Mitrović, Some covariant and contravariant fixed point theorems over bipolar p-metric spaces and applications, Filomat, 36 (5), 2022.
  • [21] A.C.M. Van Rooij, Non-Archimedean functional analysis, Dekker, New York, 1978.
  • [22] L. Zhang, J. Shen and J. Yang, G. Li, Analyzing the Fitch method for reconstructing ancestral states on ultrametric phylogenetic trees, Bull. Math. Biology 72 (7), 1760- 1782, 2010.

Characterization of bipolar ultrametric spaces and fixed point theorems

Year 2023, Volume: 52 Issue: 1, 185 - 196, 15.02.2023

Selim Çetin Utku Gürdal

https://doi.org/10.15672/hujms.1024696
Cited By: 1

Abstract

Ultrametricity condition on bipolar metric spaces is considered and a geometric characterization of bipolar ultrametric spaces is given. Also embedding a bipolar ultrametric space into a pseudo-ultrametric space is discussed and, some conditions are found to be able to embed them into an ultrametric space. Finally, some fixed point theorems on bipolar ultrametric spaces are proven.

Keywords

ultrametric space fixed point theorem bipolar metric space

References

  • [1] C. Alaca, M.E. Ege and C. Park, Fixed point results for modular ultrametric spaces, J. Comput. Anal. Appl. 20 (7), 1259–1267, 2016.
  • [2] P. Alexandroff, Zur Begründung der n-dimensionalen mengentheoretischen Topologie, Math. Ann. 94 (1), 296–308, 1925.
  • [3] M. Aschbacher, P. Baldi, E.B. Baum and R.M. Wilson, Embeddings of ultrametric spaces in finite dimensional structures, SIAM J. Algebraic Discrete Methods 8 (4), 564–577, 1987.
  • [4] U. Gürdal, Çift kutuplu metrik uzaylar ve sabit nokta teoremleri (PhD Thesis), Manisa Celâl Bayar Üniversitesi Fen Bilimleri Enstitüsü, Manisa, Türkiye, 2018.
  • [5] U. Gürdal, A. Mutlu and K. Özkan, Fixed point results for $\alpha\psi$-contractive mappings in bipolar metric spaces, J. Inequal. Spec. Funct. 11 (1), 64–75, 2020.
  • [6] J.E. Holy, Pictures of ultrametric spaces, the p-adic numbers, and valued fields, The American Mathematical Monthly 108 (8), 721–728, 2001.
  • [7] L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2), 1468–1476, 2007.
  • [8] B. Hughes, Trees and ultrametric spaces: a categorical equivalence, Adv. Math. 189 (1), 148–191, 2004.
  • [9] F. Murtagh, On ultrametricity, data coding, and computation, J. Classification 21 (2), 167–184, 2004.
  • [10] P.P. Murthy, Z. Mitrović, C.P. Dhuri and S. Radenović, The common fixed points in a bipolar metric space, Gulf J. Math. 12 (2), 31–38, 2022.
  • [11] A. Mutlu and U. Gürdal, Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl. 9 (9), 5362–5373, 2016.
  • [12] A. Mutlu, U. Gürdal and K. Özkan, Fixed point theorems for multivalued mappings on bipolar metric spaces, Fixed Point Theory 21 (1), 271–280, 2020.
  • [13] A. Mutlu, U. Gürdal and K. Özkan, Coupled fixed point theorems on bipolar metric spaces, Eur. J. Pure Appl. Math. 10 (4), 655–667, 2017.
  • [14] A. Mutlu, K. Özkan and U. Gürdal, Locally and weakly contractive principle in bipolar metric spaces, TWMS J. Appl. Eng. Math. 10 (2), 379–388, 2020.
  • [15] A.T. Ogielski and D.L. Stein, Dynamics on ultrametric spaces, Phys. Rev. Lett. 55 (15), 1634, 1985.
  • [16] K. Özkan and U. Gürdal, The fixed point theorem and characterization of bipolar metric completeness, Konuralp J. Math. 8 (1), 137–143, 2020.
  • [17] K. Özkan, U. Gürdal and A. Mutlu, Caristi’s and Downing-Kirk’s fixed point theorems on bipolar metric spaces, Fixed Point Theory, 22 (2), 785–794, 2021.
  • [18] 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), 707–714, 2020.
  • [19] R. Rammal, G. Toulouse and M.A. Virasoro, Ultrametricity for physicists, Rev. Modern Phys. 58 (3), 765, 1986.
  • [20] K. Roy, M. Saha, R. George, L. Guran and Z.D. Mitrović, Some covariant and contravariant fixed point theorems over bipolar p-metric spaces and applications, Filomat, 36 (5), 2022.
  • [21] A.C.M. Van Rooij, Non-Archimedean functional analysis, Dekker, New York, 1978.
  • [22] L. Zhang, J. Shen and J. Yang, G. Li, Analyzing the Fitch method for reconstructing ancestral states on ultrametric phylogenetic trees, Bull. Math. Biology 72 (7), 1760- 1782, 2010.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Selim Çetin 0000-0002-9017-1465

Utku Gürdal 0000-0003-2887-2188

Publication Date February 15, 2023
Published in Issue Year 2023 Volume: 52 Issue: 1

Cite

APA Çetin, S., & Gürdal, U. (2023). Characterization of bipolar ultrametric spaces and fixed point theorems. Hacettepe Journal of Mathematics and Statistics, 52(1), 185-196. https://doi.org/10.15672/hujms.1024696
AMA Çetin S, Gürdal U. Characterization of bipolar ultrametric spaces and fixed point theorems. Hacettepe Journal of Mathematics and Statistics. February 2023;52(1):185-196. doi:10.15672/hujms.1024696
Chicago Çetin, Selim, and Utku Gürdal. “Characterization of Bipolar Ultrametric Spaces and Fixed Point Theorems”. Hacettepe Journal of Mathematics and Statistics 52, no. 1 (February 2023): 185-96. https://doi.org/10.15672/hujms.1024696.
EndNote Çetin S, Gürdal U (February 1, 2023) Characterization of bipolar ultrametric spaces and fixed point theorems. Hacettepe Journal of Mathematics and Statistics 52 1 185–196.
IEEE S. Çetin and U. Gürdal, “Characterization of bipolar ultrametric spaces and fixed point theorems”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 1, pp. 185–196, 2023, doi: 10.15672/hujms.1024696.
ISNAD Çetin, Selim - Gürdal, Utku. “Characterization of Bipolar Ultrametric Spaces and Fixed Point Theorems”. Hacettepe Journal of Mathematics and Statistics 52/1 (February 2023), 185-196. https://doi.org/10.15672/hujms.1024696.
JAMA Çetin S, Gürdal U. Characterization of bipolar ultrametric spaces and fixed point theorems. Hacettepe Journal of Mathematics and Statistics. 2023;52:185–196.
MLA Çetin, Selim and Utku Gürdal. “Characterization of Bipolar Ultrametric Spaces and Fixed Point Theorems”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 1, 2023, pp. 185-96, doi:10.15672/hujms.1024696.
Vancouver Çetin S, Gürdal U. Characterization of bipolar ultrametric spaces and fixed point theorems. Hacettepe Journal of Mathematics and Statistics. 2023;52(1):185-96.

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