Some common fixed-point and fixed-figure results with a function family on $ S_{b} $-metric spaces

In this paper, we prove a common fixed-point theorem for four self-mappings with a function family on $ S_{b} $-metric spaces. In addition, we investigate some geometric properties of the fixed-point set of a given self-mapping. In this context, we obtain a fixed-disc (resp. fixed-circle), fixed-ellipse, fixed-hyperbola, fixed-Cassini curve and fixed-Apollonious circle theorems on $ S_{b} $-metric spaces.