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Some fixed point results are futile for the metric spaces with finite diameter. (English) Zbl 1479.54071

Author’s abstract: In this short note, we state some crucial facts which have to be accompanied in a series of results in the literature. Furthermore, the aim of this paper is to warn researchers to be cautious in modeling different problems governed by expansive or contractive type mappings, in the setting of a bounded metric space.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
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