Suzuki-Berinde type fixed-point and fixed-circle results on $S$-metric spaces

In this paper, the notions of a Suzuki-Berinde type $F_{S}$-contraction and a 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 a complete $S$-metric space and a fixed-circle theorem is established on a $S$-metric space. Some examples are given to support the obtained results.