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Iranian Journal of Fuzzy Systems، جلد ۹، شماره ۴، صفحات ۱۵۱-۱۵۸
عنوان فارسی ON COMPACTNESS AND G-COMPLETENESS IN FUZZY METRIC SPACES
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 di
erent 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 di
erent 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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