An Overview of Triple-Composed $S$-Metric Spaces with Few Fixed-Point Theorems

Year 2025, Volume: 8 Issue: 3, 169 - 179, 30.09.2025

Nihal Taş

https://doi.org/10.33401/fujma.1623200

Abstract

Metric fixed-point theory has received a lot of recent attention. The Banach fixed-point theorem served as the foundation for this theory. This theorem's generalizations have been looked at using various methodologies. One of these entails generalizing the prevalent contractive condition, while the other involves generalizing the prevalent metric space. Numerous generalized metric spaces were defined in the literature for the second generalization. As a new generalization of both a metric and an $S$-metric space in this context, our major goal is to present the idea of a triple-composed $S$% -metric space. We also provide some fundamental and topological ideas about triple-composed $S$-metric space. We look into some of this idea's characteristics. On triple-composed $S$-metric spaces, we demonstrate various fixed-point theorems. Finally, we provide the system of linear equations with an application.

Keywords

Triple-composed $S$-metric , Banach contraction principle , Nemytskii-Edelstein , Fixed point

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