Some remarks on fuzzy contractive mappings

Recently a new concept of fuzzy contraction in fuzzy metric spaces in the sense of George and Veeramani (Wardowski, 2013 [5]) has been introduced. Here we provide some comments to this paper.Juan-Jose Minana acknowledges the support of Conselleria de Educacion, Formacion y Empleo (Programa Vali+d para investigadores en formacion) of Generalitat Valenciana, Spain and the support of Universitat Politecnica de Valencia under Grant PAID-06-12 SP20120471.Gregori Gregori, V.; Miñana, J. (2014). Some remarks on fuzzy contractive mappings. Fuzzy Sets and Systems. 251:101-103. https://doi.org/10.1016/j.fss.2014.01.002S10110325

Common Fixed Point Theorem for ψ-weakly commuting maps in L-Fuzzy Metric Spaces for integral type

Abstract In this paper, we proved a common fixed point theorem ψ-weakly commuting maps in L-Fuzzy Metric Spaces for integral type inequality. 2010 Mathematics Subject Classification: 47H10, 54H25. Key words and phrases: L-fuzzy metric space,  ψ-weakly commuting maps, Common fixed point  theorem

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

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

A note on local bases and convergence in fuzzy metric spaces

In the context of fuzzy metrics in the sense of George and Veeramani, we study when certain families of open balls centered at a point are local bases at this point. This question is related to p-convergence and s-convergence. © 2013 Elsevier B.V. All rights reserved.Samuel Morillas acknowledges the support of Universitat Politenica de Valencia under Grant PAID-05-12 SP20120696.Gregori Gregori, V.; Miñana Prats, JJ.; Morillas Gómez, S. (2014). A note on local bases and convergence in fuzzy metric spaces. Topology and its Applications. 163:142-148. https://doi.org/10.1016/j.topol.2013.10.013S14214816

PROPERTIES OF FUZZY DITANCE ON FUZZY SET

In this paper we introduce the definition of fuzzy distance space on fuzzy set then we study and discuss several properties of  this space after some illustrative examples are given . Furthermore we introduce the definition of fuzzy convergence, fuzzy Cauchy sequence of fuzzy point and fuzzy bounded fuzzy distance space .&nbsp

Fixed Point Theorem for Fuzzy Contractive Mappings in Fuzzy Metric Spaces

Abstract In this paper we give a fixed-point theorem for fuzzy contractive mappings in the George and Veeramani p-complete fuzzy metric spaces

FUZZY COMPACT FUZZY DISTANCE SPACE

In this paper we recall the definition of fuzzy distance space on a fuzzy set then we define a compact fuzzy distance space and fuzzy totally bounded after that we prove that fuzzy totally bounded fuzzy complete fuzzy distance space is fuzzy compact. Moreover we recall the definition of fuzzy continuous and uniform fuzzy continuous function to prove that fuzzy continuous function and uniform fuzzy continuous functions are equivalent on a fuzzy compact fuzzy distance spaces