Fixed point theorems and Cauchy sequences in fuzzy metric spaces (Q1874071)

One can find several definitions of the concept of a Cauchy sequence in a fuzzy metric space in the sense of Kramosil and Michalek. This paper presents an example illustrating that definitions given by \textit{M. Grabiec} [ibid. 27, 385-389 (1989; Zbl 0664.54032)] and \textit{R. Vasuki} [ibid. 97, 395-397 (1998; Zbl 0960.54005)] are not equivalent to the definition of George and Veeramani. This fact explains in particular why ``fixed point type'' theorems proved by different authors (see e.g., papers by M. Grabiec, V. Gregori and A. Sapena and R. Vasuki) sometimes have a different ``shape''.