Document Type: Research Paper


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


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


Main Subjects

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