New generalized fuzzy metrics and fixed point theorem in fuzzy metric space

Plebaniak, Robert

dc.contributor.author	Plebaniak, Robert
dc.date.accessioned	2015-04-13T07:49:44Z
dc.date.available	2015-04-13T07:49:44Z
dc.date.issued	2014-12-08
dc.identifier.issn	1687-1812
dc.identifier.uri	http://hdl.handle.net/11089/7874
dc.description.abstract	In this paper, in fuzzy metric spaces (in the sense of Kramosil and Michalek (Kibernetika 11:336-344, 1957)) we introduce the concept of a generalized fuzzy metric which is the extension of a fuzzy metric. First, inspired by the ideas of Grabiec (Fuzzy Sets Syst. 125:385-389, 1989), we define a new G-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by M Grabiec). Next, inspired by the ideas of Gregori and Sapena (Fuzzy Sets Syst. 125:245-252, 2002), we define a new GV-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by V Gregori and A Sapena). Moreover, we provide the condition guaranteeing the existence of a fixed point for these single-valued contractions. Next, we show that the generalized pseudodistance J:X×X→[0,∞) (introduced by Włodarczyk and Plebaniak (Appl. Math. Lett. 24:325-328, 2011)) may generate some generalized fuzzy metric NJ on X. The paper includes also the comparison of our results with those existing in the literature.	pl_PL
dc.language.iso	en	pl_PL
dc.publisher	Springer	pl_PL
dc.relation.ispartofseries	Fixed Point Theory and Applications;2014:241
dc.rights	Uznanie autorstwa 3.0 Polska	*
dc.rights.uri	http://creativecommons.org/licenses/by/3.0/pl/	*
dc.subject	fuzzy sets	pl_PL
dc.subject	fuzzy metric space	pl_PL
dc.subject	contraction of Banach type	pl_PL
dc.subject	fixed point	pl_PL
dc.subject	generalized fuzzy metrics	pl_PL
dc.subject	fuzzy metrics	pl_PL
dc.title	New generalized fuzzy metrics and fixed point theorem in fuzzy metric space	pl_PL
dc.type	Article	pl_PL
dc.page.number	1-17	pl_PL
dc.contributor.authorAffiliation	University of Łódz, Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science	pl_PL
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dc.contributor.authorEmail	robpleb@math.uni.lodz.pl	pl_PL