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.
Citation: Nihal Taş, Irshad Ayoob, Nabil Mlaiki. Some common fixed-point and fixed-figure results with a function family on $ S_{b} $-metric spaces[J]. AIMS Mathematics, 2023, 8(6): 13050-13065. doi: 10.3934/math.2023657
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.
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Nihal Taş, Irshad Ayoob, Nabil Mlaiki. Some common fixed-point and fixed-figure results with a function family on $ S_{b} $-metric spaces[J]. AIMS Mathematics, 2023, 8(6): 13050-13065. doi: 10.3934/math.2023657
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