An introduction to fixed-circle problem on soft metric spaces

Abstract

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.