Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 9 Sayı: 1, 33 - 39, 28.04.2021

Öz

Kaynakça

  • [1] A. Aliouche, C.Simpson, Fixed Points and Lines in 2-Metric Spaces, Advances In Math. Vol: 229 (2012) 668-690.
  • [2] I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. Vol: 30 (1989), 26-37.
  • [3] S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica Et Informatica Universitatis Ostraviensis Vol: 1 (1993), 5-11.
  • [4] M. R. Farhangdoost, Metrizable and 2-Metrizable Topological Spaces, Journal of Dynamical Systems and Geometric Theories Vol: 10 (2012), 61-69.
  • [5] S. Gahler,¨ 2-Metrische Raume¨ und ihre topologische struktur, Math. Nachr. Vol:26 (1963), 115-118.
  • [6] S. Gahler,¨ Lineare 2-normierte Raume,¨ Math. Nachr. Vol: 28 (1965), 1-43.
  • [7] S. Gahler,¨ W. Gahler,¨ Espaces 2-Metriques Et Localement 2-Metriques, Ann.Scient.Ec.Norm.Sup. Vol: 3 (1965), 387-395
  • [8] K. Iseki, Fixed point theorems in 2-metric spaces, Math. Seminar Notes, Kobe Univ. Vol: 3 (1975) 133-136.
  • [9] M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Analysis: Theory, Methods and Applications Vol: 73 No: 9 (2010), 3123-3129.
  • [10] W. Kirk, N. Shahzad, Fixed Point Theory in Distance Spaces, Springer, Cham (2014).
  • [11] B. K. Lahiri, P.Das, L.K.Dey, Cantor’s theorem in 2-metric spaces and its applications to fixed point problems, Taiwanese J.Math. Vol: 15 (2011) 337-352.
  • [12] Z. Mustafa, V. Parvaech, J. R. Roshan, Z. Kadelburg, b2-Metric Spaces and Some Fixed Point Theorems, Fixed Point Theory and Applications Vol: 144 (2014).
  • [13] S. V. R. Naidu, J. Rajendra Prasad, Fixed point theorems in 2-metric space, Indian J.Pure Appl.Math. Vol: 17 No: 8 (1986) 974-993.
  • [14] T. Van An, L. Q. Tuyen, N. Van Dung, Stone-type theorem on b-metric spaces and applications, Topology and its Applications Vol: 185 (2015) 50-64.

On $b_2$-Metric Spaces

Yıl 2021, Cilt: 9 Sayı: 1, 33 - 39, 28.04.2021

Öz

The target of this paper is to induce a topology from a given $b_2$-metric and study the properties of the topology induced by this way. We first define the notion of $\varepsilon$-ball in $b_2$-metric spaces and consider the topology induced by a given $b_2$-metric via $\varepsilon$-balls. We study some properties of this topological space such as separation axioms and semi-metrizability. Also, we show with the examples that some known properties for $\varepsilon$-balls in metric spaces have not existed in $b_2$-metric spaces. Then we introduce the concept of strong $b_2$-metric spaces in which these known properties are provided. Finally, we show that every strong $b_2$-metric topological space is normal, metrizable and of second category.

Kaynakça

  • [1] A. Aliouche, C.Simpson, Fixed Points and Lines in 2-Metric Spaces, Advances In Math. Vol: 229 (2012) 668-690.
  • [2] I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. Vol: 30 (1989), 26-37.
  • [3] S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica Et Informatica Universitatis Ostraviensis Vol: 1 (1993), 5-11.
  • [4] M. R. Farhangdoost, Metrizable and 2-Metrizable Topological Spaces, Journal of Dynamical Systems and Geometric Theories Vol: 10 (2012), 61-69.
  • [5] S. Gahler,¨ 2-Metrische Raume¨ und ihre topologische struktur, Math. Nachr. Vol:26 (1963), 115-118.
  • [6] S. Gahler,¨ Lineare 2-normierte Raume,¨ Math. Nachr. Vol: 28 (1965), 1-43.
  • [7] S. Gahler,¨ W. Gahler,¨ Espaces 2-Metriques Et Localement 2-Metriques, Ann.Scient.Ec.Norm.Sup. Vol: 3 (1965), 387-395
  • [8] K. Iseki, Fixed point theorems in 2-metric spaces, Math. Seminar Notes, Kobe Univ. Vol: 3 (1975) 133-136.
  • [9] M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Analysis: Theory, Methods and Applications Vol: 73 No: 9 (2010), 3123-3129.
  • [10] W. Kirk, N. Shahzad, Fixed Point Theory in Distance Spaces, Springer, Cham (2014).
  • [11] B. K. Lahiri, P.Das, L.K.Dey, Cantor’s theorem in 2-metric spaces and its applications to fixed point problems, Taiwanese J.Math. Vol: 15 (2011) 337-352.
  • [12] Z. Mustafa, V. Parvaech, J. R. Roshan, Z. Kadelburg, b2-Metric Spaces and Some Fixed Point Theorems, Fixed Point Theory and Applications Vol: 144 (2014).
  • [13] S. V. R. Naidu, J. Rajendra Prasad, Fixed point theorems in 2-metric space, Indian J.Pure Appl.Math. Vol: 17 No: 8 (1986) 974-993.
  • [14] T. Van An, L. Q. Tuyen, N. Van Dung, Stone-type theorem on b-metric spaces and applications, Topology and its Applications Vol: 185 (2015) 50-64.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Elif Güner 0000-0002-6969-400X

Halis Aygün 0000-0003-3263-3884

Yayımlanma Tarihi 28 Nisan 2021
Gönderilme Tarihi 21 Mayıs 2020
Kabul Tarihi 8 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 9 Sayı: 1

Kaynak Göster

APA Güner, E., & Aygün, H. (2021). On $b_2$-Metric Spaces. Konuralp Journal of Mathematics, 9(1), 33-39.
AMA Güner E, Aygün H. On $b_2$-Metric Spaces. Konuralp J. Math. Nisan 2021;9(1):33-39.
Chicago Güner, Elif, ve Halis Aygün. “On $b_2$-Metric Spaces”. Konuralp Journal of Mathematics 9, sy. 1 (Nisan 2021): 33-39.
EndNote Güner E, Aygün H (01 Nisan 2021) On $b_2$-Metric Spaces. Konuralp Journal of Mathematics 9 1 33–39.
IEEE E. Güner ve H. Aygün, “On $b_2$-Metric Spaces”, Konuralp J. Math., c. 9, sy. 1, ss. 33–39, 2021.
ISNAD Güner, Elif - Aygün, Halis. “On $b_2$-Metric Spaces”. Konuralp Journal of Mathematics 9/1 (Nisan 2021), 33-39.
JAMA Güner E, Aygün H. On $b_2$-Metric Spaces. Konuralp J. Math. 2021;9:33–39.
MLA Güner, Elif ve Halis Aygün. “On $b_2$-Metric Spaces”. Konuralp Journal of Mathematics, c. 9, sy. 1, 2021, ss. 33-39.
Vancouver Güner E, Aygün H. On $b_2$-Metric Spaces. Konuralp J. Math. 2021;9(1):33-9.
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