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Research Article | Open Access

Some common fixed-point and fixed-figure results with a function family on S b -metric spaces

Nihal Taş1, Irshad Ayoob2, Nabil Mlaiki2( )
Balıkesir University, Department of Mathematics, Balıkesir 10145, Tü rkiye
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
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Abstract

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.

Keywords

Sb-metricfixed pointfixed figure
CLC number: 47H09, 47H10, 54H25

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AIMS Mathematics
Volume 8 Issue 6,
June 2023
Pages 13050-13065
DOI: 10.3934/math.2023657

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Cite this article:
Taş N, Ayoob I, Mlaiki N. Some common fixed-point and fixed-figure results with a function family on S b -metric spaces. AIMS Mathematics, 2023, 8(6): 13050-13065. https://doi.org/10.3934/math.2023657

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Received: 18 February 2023
Revised: 22 March 2023
Accepted: 23 March 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)