The notion of a metric space is an important tool in functional analysis, nonlinear analysis and especially in topology. New generalizations of metric spaces have been introduced in recent years. For instance, $S$-metric and $b$-metric spaces are among the recent generalizations of a metric space. Fixed point theory has been intensively studied and generalized using various approaches on these new spaces. In this paper we consider the relationships among a metric, an $S$-metric and a $b$-metric. In this context, we define the topological equivalence between a metric and an $S$-metric. Especially, we focus on the fact that every $S$-metric does not always generate a metric. This is the main motivation of the recent fixed point studies for self-mappings on an $S$-metric space. Also we revisit the notion of a metric generated by an $S$-metric. We support our theoretical findings by necessary illustrative examples. As a consequence, existing studies based on the metric generated by an S-metric can be updated using a general $S$-metric whether generate a metric or not.
OZGUR, N., & TAS, N. (2023). On $S$-metric spaces with some topological aspects. Electronic Journal of Mathematical Analysis and Applications, 11(2), 1-8. doi: 10.21608/ejmaa.2023.206319.1029
MLA
Nihal OZGUR; Nihal TAS. "On $S$-metric spaces with some topological aspects". Electronic Journal of Mathematical Analysis and Applications, 11, 2, 2023, 1-8. doi: 10.21608/ejmaa.2023.206319.1029
HARVARD
OZGUR, N., TAS, N. (2023). 'On $S$-metric spaces with some topological aspects', Electronic Journal of Mathematical Analysis and Applications, 11(2), pp. 1-8. doi: 10.21608/ejmaa.2023.206319.1029
VANCOUVER
OZGUR, N., TAS, N. On $S$-metric spaces with some topological aspects. Electronic Journal of Mathematical Analysis and Applications, 2023; 11(2): 1-8. doi: 10.21608/ejmaa.2023.206319.1029
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