Cauchyness and convergence in fuzzy metric spaces

In this paper we survey some concepts of convergence and Cauchyness appeared separately in the context of fuzzy metric spaces in the sense of George and Veeramani. For each convergence (Cauchyness) concept we find a compatible Cauchyness (convergence) concept. We also study the relationship among them and the relationship with compactness and completeness (defined in a natural sense for each one of the Cauchy concepts). In particular, we prove that compactness implies p-completeness.

[1]  H. Sherwood,et al.  On the completion of probabilistic metric spaces , 1966 .

[2]  V. Gregori,et al.  On Banach contraction principles in fuzzy metric spaces , 2018 .

[3]  Dorel Mihet,et al.  On Fuzzy -Contractive Mappings in Fuzzy Metric Spaces , 2007, Fuzzy Sets Syst..

[4]  Valentín Gregori,et al.  Strong Convergence in Fuzzy Metric Spaces , 2017 .

[5]  Valentín Gregori,et al.  Characterizing completable fuzzy metric spaces , 2004, Fuzzy Sets Syst..

[6]  Mariusz Grabiec,et al.  Fixed points in fuzzy metric spaces , 1988 .

[7]  Samuel Morillas,et al.  On convergence in fuzzy metric spaces , 2009 .

[8]  Jin-xuan Fang,et al.  On fixed point theorems in fuzzy metric spaces , 1992 .

[9]  Ramakant Bhardwaj,et al.  On Fixed Point theorems in Fuzzy Metric Spaces , 2013 .

[10]  Samuel Morillas,et al.  Some questions in fuzzy metric spaces , 2012, Fuzzy Sets Syst..

[11]  Valentín Gregori,et al.  On completion of fuzzy metric spaces , 2002, Fuzzy Sets Syst..

[12]  Samuel Morillas,et al.  Examples of fuzzy metrics and applications , 2011, Fuzzy Sets Syst..

[13]  Valentín Gregori,et al.  std-Convergence in fuzzy metric spaces , 2015, Fuzzy Sets Syst..

[14]  Salvador Romaguera,et al.  A domain-theoretic approach to fuzzy metric spaces , 2014 .

[15]  Dorel Mihet,et al.  A Banach contraction theorem in fuzzy metric spaces , 2004, Fuzzy Sets Syst..

[16]  Dorel Miheţ.  On Fuzzy -Contractive Mappings in Fuzzy Metric Spaces , 2007 .

[17]  Saranjit Singh,et al.  Common fixed points of maps on fuzzy metric spaces , 1994 .

[18]  A. George,et al.  On some results in fuzzy metric spaces , 1994 .

[19]  P. Veeramani,et al.  Fixed point theorems and Cauchy sequences in fuzzy metric spaces , 2003, Fuzzy Sets Syst..

[20]  Valentín Gregori,et al.  Fixed point theorems for fuzzy mappings in quasi-metric spaces , 2000, Fuzzy Sets Syst..

[21]  Samuel Morillas,et al.  On a class of completable fuzzy metric spaces , 2010, Fuzzy Sets Syst..

[22]  Pedro Tirado,et al.  ON COMPACTNESS AND G-COMPLETENESS IN FUZZY METRIC SPACES , 2012 .

[23]  C. T. Aage,et al.  On Fixed Point Theorems in Fuzzy Metric Spaces , 2010 .

[24]  H. Sherwood,et al.  Complete probabilistic metric spaces , 1971 .

[25]  Naser Abbasi,et al.  On best approximation in fuzzy metric spaces , 2015, Kybernetika.

[26]  C. Alaca,et al.  Fixed points in intuitionistic fuzzy metric spaces , 2006 .

[27]  Valentín Gregory,et al.  Some properites of fuzzy metric spaces , 2000 .

[28]  P. Veeramani,et al.  On some results of analysis for fuzzy metric spaces , 1997, Fuzzy Sets Syst..

[29]  Ivan Kramosil,et al.  Fuzzy metrics and statistical metric spaces , 1975, Kybernetika.

[30]  Samuel Morillas,et al.  On completable fuzzy metric spaces , 2015, Fuzzy Sets Syst..

[31]  Pedro Tirado Peláez.  Contraction mappings in fuzzy quasi-metric spaces and [0,1]-fuzzy posets , 2012 .

[32]  Abbas Edalat,et al.  A Computational Model for Metric Spaces , 1998, Theor. Comput. Sci..

[33]  Valentín Gregori,et al.  Some properties of fuzzy metric spaces , 2000, Fuzzy Sets Syst..

[34]  Dorel Mihet,et al.  Fuzzy psi-contractive mappings in non-Archimedean fuzzy metric spaces , 2008, Fuzzy Sets Syst..

[35]  Pedro Tirado,et al.  CONTRACTION MAPPINGS IN FUZZY QUASI-METRIC SPACES AND (0,1)-FUZZY POSETS , 2012 .

[36]  Samuel Morillas,et al.  A note on convergence in fuzzy metric spaces , 2014 .