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On multiplicative metric spaces: survey. (English) Zbl 1458.54035

Summary: The purpose of this survey is to prove that the fixed point results for various multiplicative contractions are in fact equivalent to the corresponding fixed point results in (standard) metric spaces. For example, such are recent results established by X. He et al. [Fixed Point Theory Appl. 2014, Paper No. 48, 9 p. (2014; Zbl 1419.54050)], C. Mongkolkeha and W. Sintunavarat [J. Nonlinear Sci. Appl. 8, No. 6, 1134–1140 (2015; Zbl 1437.54059)] and A. A. N. Abdou [J. Nonlinear Sci. Appl. 9, No. 5, 2347–2363 (2016; Zbl 1338.54148)] and all others from the list of references. Our results here generalize, complement, and improve recent ones from existing literature.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54E35 Metric spaces, metrizability
54-02 Research exposition (monographs, survey articles) pertaining to general topology
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