Description

• Title:
  New generalized fuzzy metrics and fixed point theorem in fuzzy metric space
• Creator:
  Plebaniak, Robert
• Contributor:
  University of Łódz, Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science;
  robpleb@math.uni.lodz.pl
• Description:
  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.
• Object availability:
  free access
• Rights:
  Uznanie autorstwa 3.0 Polska;
  http://creativecommons.org/licenses/by/3.0/pl
• Date:
  2015.04.13;
  2014.12.08
• Type:
  Article
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Springer
• Relation:
  Fixed Point Theory and Applications;2014:241
• Subject:
  fuzzy sets;
  fuzzy metric space;
  contraction of Banach type;
  fixed point;
  generalized fuzzy metrics;
  fuzzy metrics
• Identifier:
  1687-1812;
  http://hdl.handle.net/11089/7874
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  image