On $S$-metric spaces with some topological aspects | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Volume 11, Issue 2, July 2023, Pages 1-8 PDF (421.36 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2023.206319.1029 | ||
| Authors | ||
| Nihal OZGUR* 1; Nihal TAS2 | ||
| 1İzmir Democracy University Department of Mathematics | ||
| 2Balıkesir University Department of Mathematics | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| $S$-metric; $b$-metric; topological equivalence; Lipschitz equivalence | ||
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