On the topological equivalence of some generalized metric spaces

Subject Areas : Fixed point theory

N. TAŞ ¹

1 - Department of Mathematics, Bali kesir University, 10145, Bali kesir, Turkey

Received: 2019-07-16 Accepted : 2020-03-17 Published : 2020-03-01

Keywords: S-metric, cone S-metric, N-cone metric,

Abstract :

‎The aim of this paper is to establish the equivalence between the concepts‎‎of an $S$-metric space and a cone $S$-metric space using some topological‎‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎‎some facts about topological vector spaces‎. ‎We see that the known results on‎‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎from the studies on $S$-metric spaces‎.

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