Recently, soft set theory has been extensively studied both theoretically and practically with different approaches. On the other hand, fixed-circle problem has been investigated as a geometric generalization of fixed-point theory and this problem can be applied to some applicable areas. With these two perspectives, in this paper, we obtain some soft fixed-circle results using different auxiliary functions on a soft metric space. To do this, we are inspired various contractive conditions. The obtained results can be considered as an existence or uniqueness theorem. The proved theorems are supported by some illustrative examples. Finally, we give a list of geometric consequences of these results.‎ Manuscript profile

In this paper, the notions of a Suzuki-Berinde type $F_{S}$-contraction anda Suzuki-Berinde type $F_{C}^{S}$-contraction are introduced on a $S$-metric space. Using these new notions, a fixed-point theorem is proved on acomplete $S$-metric space and a fixed-circle theorem is established on a $S$-metric space. Some examples are given to support the obtained results. Manuscript profile

‎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. Manuscript profile