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\(S\)-\(\gamma\)-\(\phi\)-\(\varphi\)-contractive type mappings in \(S\)-metric spaces. (English) Zbl 1412.47199

Summary: In this paper, we introduce several types of \(S\)-\(\gamma\)-\(\phi\)-\(\varphi\)-contractive mappings which are generalizations of \(\alpha\)-\(\psi\)-contractive mappings [B. Samet et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 2154–2165 (2012; Zbl 1242.54027)] in the context of \(S\)-metric spaces. Furthermore, we prove existence and uniqueness of fixed points and common fixed points of such contractive mappings. Our results generalize, extend and improve the existing results in the literature. We also state some illustrative examples to support our results.

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
54E50 Complete metric spaces

Citations:

Zbl 1242.54027
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References:

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