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Iranian Journal of Fuzzy Systems، جلد ۹، شماره ۴، صفحات ۱۵۱-۱۵۸
عنوان فارسی
چکیده فارسی مقاله In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case, for which we present an example of a compact fuzzy metric space that is not complete in Grabiecs sense. On the other hand, Grabiec used a notion of compactness to obtain a fuzzy version of Edelstein s contraction principle. We present here a generalized version of Grabiecs version of the Edelstein xed point theorem and dierent interesting facts on the topology of fuzzy metric spaces.
کلیدواژه‌های فارسی مقاله Fuzzy metric space، Cauchy sequence، G-completeness، Compactness، Fixed point theorem،
عنوان انگلیسی ON COMPACTNESS AND G-COMPLETENESS IN FUZZY METRIC SPACES
چکیده انگلیسی مقاله In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case, for which we present an example of a compact fuzzy metric space that is not complete in Grabiecs sense. On the other hand, Grabiec used a notion of compactness to obtain a fuzzy version of Edelstein s contraction principle. We present here a generalized version of Grabiecs version of the Edelstein xed point theorem and dierent interesting facts on the topology of fuzzy metric spaces.
کلیدواژه‌های انگلیسی مقاله Fuzzy metric space, Cauchy sequence, G-completeness, Compactness, Fixed point theorem
نویسندگان مقاله Pedro Tirado |
Instituto Universitario de Matematica Pura y Aplicada, Universidad Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

نشانی اینترنتی http://ijfs.usb.ac.ir/article_139_bcc0473d0d21e8f848502062a387e278.pdf
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