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Zbl 0579.54034
Chang, Shihsen
Fixed point theorems for fuzzy mappings.
(English)
[J] Fuzzy Sets Syst. 17, 181-187 (1985). ISSN 0165-0114

This paper contains some fixed point theorems for fuzzy mappings $F$ and $G : X \to \cal W(X)$, $X$ a complete metric space and $\cal W(X)$ the subcollectionof all fuzzy sets in $X$, satisfying the following condition of generalized contractive type $$H(\tilde F(x),\tilde G(y)) \le \Phi\left( d(x,y), d(x,\tilde F(x)), d(y,\tilde G(y)), d(x,\tilde G(y)), d(y,\tilde F(x)) \right),\quad x,y\in X,$$ where the function $\Phi$ is a suitable nonnegative real function. Then under certain hypotheses on $F$, $G$ and $\Phi$ three results on the existence of a fixed point are shown. The results improve and extend some results of {\it S. Heilpern} [J. Math. Anal. Appl. 83, 566-569 (1981; Zbl 0486.54006)], {\it D. Butnariu} [Fuzzy Sets Syst. 7, 191-207 (1982; Zbl 0473.90087)], and the author [Appl. Math. Mech., Engl. Ed. 5, 1273- 1279 (1984; Zbl 0549.54034)].
MSC 2000:
*54H25 Fixed-point theorems in topological spaces
54A40 Fuzzy topology

Keywords: fuzzy mappings

Citations: Zbl 0486.54006; Zbl 0473.90087; Zbl 0549.54034

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