Rational Type Fixed-Disc and Common Fixed-Disc Results on Metric and S-Metric Spaces via Geraghty Type Contractions

Abstract

This work aims to extend the Geraghty fixed point results motivated by the approach of rational-type contractions. We introduce the class of rational Geraghty contraction (RGC) of type I, II, III and provide the related fixed-disc (fixed-circle) results in metric spaces (MS) and S-metric spaces (S-MS). We also derive common fixed disc (fixed circle) results for these contractions. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.