Elsevier

Fuzzy Sets and Systems

Volume 157, Issue 2, 16 January 2006, Pages 270-285
Fuzzy Sets and Systems

On fixed degree theorems for fuzzy mappings in Menger PM-spaces

https://doi.org/10.1016/j.fss.2005.06.019Get rights and content

Abstract

In this paper, we establish a new common fixed degree theorem for a sequence of fuzzy mappings in Menger PM-spaces. As an immediate consequence of this theorem, we obtain an improvement of a corresponding result of Chang et al. (Fuzzy Sets and Systems 87 (1997) 325–334). In addition, we also obtain some fixed degree and fixed point theorems for fuzzy mappings in fuzzy metric spaces. Our results unify and generalize the results of Heilpern (J. Math. Anal. Appl. 83 (1981) 566–569), Butnariu (Fuzzy Sets and Systems 7 (1982) 191–207), Hadžíc (Fuzzy Sets and Systems 29 (1989) 115–125), Fang (Fuzzy Sets and Systems 48 (1992) 391–395), Lee et al. (Fuzzy Sets and Systems 61 (1994) 309–312; J. Fuzzy Math. 2 (1994) 859–870) and Chang et al. (Math. Japon. 40 (1994) 289–293; Fuzzy Sets and Systems 87 (1997) 325–334).

References (23)

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      Citation Excerpt :

      Fixed point theory in probabilistic metric spaces can be considered as a part of probabilistic analysis, which is a very dynamic area of mathematical research (see [7]). The fixed point theorems for some contraction mappings and generalized contraction mappings in probabilistic metric spaces were investigated by many authors, such as Chang [3], Fang [4,5], Hadžíc et al. [7–9], Hicks [10], Liu and Li [14], Mihet [16–19], Pap and Hadžíc [25], Razani and Fouladgar [26], Sehgal and Bharucha-Reid [27], Singh et al. [28,29] and Žikić-Došenvić [33]. However, we rarely see any work about fixed point theorems of mappings under strict contractive conditions in probabilistic metric spaces.

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