Abstract: In this paper, we investigate new fixed-point results within the framework of S-metric spaces, which provide a significant generalization of classical metric spaces. We introduce and utilize a Chatterjea type contractive condition involving altering distance functions, denoted by  , to establish the existence and uniqueness of fixed points. Specifically, we prove two primary theorems: the first considers self-mappings on T -orbitally compact S-metric spaces where the mapping is orbitally continuous, and the second extends these results to boundedly compact S-metric spaces. To support our theoretical findings, we provide illustrative examples of S-metrics that are not generated by any traditional metric, demonstrating the broader applicability of our results. Additionally, we present corollaries that translate these findings into the context of b-metric spaces generated by S-metrics.

Keywords: fixed point, S-metric space, Chatterjea type contraction, orbitally compact, orbitally continuous, boundedly compact

Pages: 563-570