Fixed degree and fixed point theorems for fuzzy mappings in probabilistic metric spaces

Abstract This paper introduces the concept and properties of fixed degrees for fuzzy mappings in probabilistic metric spaces. By virtue of this concept, some theorems about common fixed degree of a sequence of fuzzy mappings in probabilistic metric spaces are obtained. These new results are a unified approach to generalize several fixed point theorems for fuzzy mappings.

[1]  B. Schweizer,et al.  The metrization of statistical metric spaces. , 1960 .

[2]  O. Hadzic,et al.  Fixed point theorems for multivalued mappings in probabilistic metric spaces , 1997, Fuzzy Sets Syst..

[3]  Stanisław Heilpern,et al.  Fuzzy mappings and fixed point theorem , 1981 .

[4]  Shih-Sen Chang.  Coincidence theorems and variational inequalities for fuzzy mappings , 1994 .

[5]  Sung Jin Cho,et al.  A fixed point theorem for contractive-type fuzzy mappings , 1994 .

[6]  O. Hadzic,et al.  Fixed point theorems for multivalued mappings in some classes of fuzzy metic spaces , 1989 .

[7]  Jin-xuan Fang,et al.  On fixed point theorems in fuzzy metric spaces , 1992 .

[8]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[9]  Dan Butnariu,et al.  Fixed points for fuzzy mappings , 1982 .

[10]  B. Schweizer,et al.  Statistical metric spaces. , 1960 .

[11]  Michael D. Weiss.  Fixed points, separation, and induced topologies for fuzzy sets , 1975 .

[12]  Chang Shih-sen.  FIXED POINT THEOREMS FOR FUZZY MAPPINGS , 1985 .

[13]  J. Fang,et al.  A note on fixed point theorems of Hadzci´c , 1992 .

[14]  Mariusz Grabiec,et al.  Fixed points in fuzzy metric spaces , 1988 .

[15]  R. K. Bose,et al.  Fuzzy mappings and fixed point theorems , 1987 .

[16]  Shih-Sen Chang.  Fixed degree for fuzzy mappings and a generalization of Ky Fan's theorem , 1987 .

[17]  Shih-Sen Chang.  Coincidence degree and coincidence theorems for fuzzy mappings , 1988 .

[18]  Osmo Kaleva,et al.  On fuzzy metric spaces , 1984 .