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Some fixed point theorems on \(S\)-metric spaces. (English) Zbl 1474.54211

Summary: 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.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E35 Metric spaces, metrizability
54E40 Special maps on metric spaces
54E45 Compact (locally compact) metric spaces
54E50 Complete metric spaces
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References:

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