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Minimization theorems for fixed point theorems in fuzzy metric spaces and applications. (English) Zbl 0845.54004

The authors prove a minimization theorem in fuzzy metric spaces. The theorem goes as follows: If \(X\) and \(Y\) are complete fuzzy metric spaces of a given type, \(f: X\to Y\) is closed and continuous and \(\varphi: f(X)\to (-\infty, \infty]\) is lower semicontinuous and bounded from below then under certain assumptions \(\varphi \circ f\) attains its minimum.
Using the theorem above the authors obtain a variational principle as well as a fixed point theorem for fuzzy metric spaces. Finally the equivalence of these theorems is proved.
The variational principle, the fixed point theorem and their equivalence also appear in M. Stojaković and Z. Ovcin [ibid. 66, 353-356 (1994; Zbl 0842.54020)].
Reviewer: O.Kaleva (Tampere)

MSC:

54A40 Fuzzy topology

Citations:

Zbl 0842.54020
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References:

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