Araştırma Makalesi
Yıl 2023,
Cilt: 52 Sayı: 1, 185 - 196, 15.02.2023
Öz
Anahtar Kelimeler
Kaynakça
- [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.
Yıl 2023,
Cilt: 52 Sayı: 1, 185 - 196, 15.02.2023
Öz
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.
Anahtar Kelimeler
Kaynakça
- [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.
Toplam 22 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 15 Şubat 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 52 Sayı: 1 |