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.

MSC: 54E35, 54E40, 54E45, 54E50

Pages:  39$-$52     

Volume  69 ,  Issue  1 ,  2017