TY  - JOUR
T1  - On $b_2$-Metric Spaces
AU  - Güner, Elif
AU  - Aygün, Halis
PY  - 2021
DA  - April
Y2  - 2021
JF  - Konuralp Journal of Mathematics
JO  - Konuralp J. Math.
PB  - Mehmet Zeki SARIKAYA
WT  - DergiPark
SN  - 2147-625X
SP  - 33
EP  - 39
VL  - 9
IS  - 1
LA  - en
AB  - 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.
KW  - b_2-metric spaces
KW  - strong b_2-metric spaces
KW  - Hausdorff Spaces
KW  - Metrizable topological spaces
CR  - [1]	A. Aliouche, C.Simpson, Fixed Points and Lines in 2-Metric Spaces, Advances In Math. Vol: 229 (2012) 668-690.
CR  - [2]	I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. Vol: 30 (1989), 26-37.
CR  - [3]	S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica Et Informatica Universitatis Ostraviensis Vol: 1 (1993), 5-11.
CR  - [4]	M. R. Farhangdoost, Metrizable and 2-Metrizable Topological Spaces, Journal of Dynamical Systems and Geometric Theories Vol: 10 (2012), 61-69.
CR  - [5]	S. Gahler,¨ 2-Metrische Raume¨ und ihre topologische struktur, Math. Nachr. Vol:26 (1963), 115-118.
CR  - [6]	S. Gahler,¨ Lineare 2-normierte Raume,¨ Math. Nachr. Vol: 28 (1965), 1-43.
CR  - [7]	S. Gahler,¨ W. Gahler,¨ Espaces 2-Metriques Et Localement 2-Metriques, Ann.Scient.Ec.Norm.Sup. Vol: 3 (1965), 387-395
CR  - [8]	K. Iseki, Fixed point theorems in 2-metric spaces, Math. Seminar Notes, Kobe Univ. Vol: 3 (1975) 133-136.
CR  - [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.
CR  - [10]	W. Kirk, N. Shahzad, Fixed Point Theory in Distance Spaces, Springer, Cham (2014).
CR  - [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.
CR  - [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).
CR  - [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.
CR  - [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.
UR  - https://dergipark.org.tr/en/pub/konuralpjournalmath/issue//740312
L1  - https://dergipark.org.tr/en/download/article-file/1112560
ER  -