Some fixed point theorems on S-metric spaces

Níhal Yilmaz Özgür and Níhal Taş

Abstract: In this paper, we present some contractive mappings and prove new generalized fixed point theorems on $S$-metric spaces. Also we define the notion of a cluster point and investigate fixed points of self-mappings using cluster points on $S$-metric spaces. We obtain new generalizations of the classical Nemytskii-Edelstein and Ćirić’s fixed point theorems for continuous self-mappings of compact $S$-metric spaces.

Keywords: $S$-metric space; fixed point theorem; $C_S$-mapping; $L_S$-mapping; cluster point.

Classification (MSC2000): 54E35; 54E40, 54E45, 54E50

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