For a class of fuzzy METRIC SPACES (in the sense of George and Veeramani) with an H-type t-norm, we present a method to construct a METRIC on a fuzzy METRIC space. The induced METRIC space shares many important properties with the given fuzzy METRIC space. Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some problems for fuzzy METRIC SPACES in the literature, which are shown by examples in this paper.

In this paper, we introduce the concept of the rectangular M-METRIC SPACES, along with its topology and we prove some fixed-point theorems under different contraction principles with various techniques. The obtained results generalize some classical fixed-point results such as the Banach’ s contraction principle, the Kannan’ s fixed-point theorem and the Chatterjea’ s fixed-point theorem. Also we give an application to the fixed-circle problem.

Many authors have introduced the concept of fuzzy METRIC SPACES in different ways. In this paper, we get a special structure for some separable fuzzy METRIC and M-fuzzy METRIC SPACES, where the METRIC space has been introduced by George and Veermani.

In this paper, we discuss the inheritance of strict convexity, uniform convexity and local uniform convexity by the quotient SPACES of METRIC linear SPACES. We also show that, as in the case of normed linear SPACES, completeness is a three-space property in METRIC linear SPACES as well.

The aim of this paper is to study induced (quasi-) uniformities in Kramosil and Michalek's fuzzy METRIC SPACES. Firstly, I-uniformity in the sense of J. Gutierrez Garcia and I-neighborhood system in the sense of Hohle and Sostak are induced by the given fuzzy METRIC. It is shown that the fuzzy METRIC and the induced I-uniformity will generate the same I-neighborhood system. Secondly, the relationship between Hutton quasi-uniformities and I-quasi-uniformities is given and it is proved that the category of strongly stratified I-quasi-uniform SPACES can be embedded in the category of Hutton quasi-uniform SPACES as a bicoreflective subcategory. Also it is shown that two kinds of Hutton quasi-uniformities can generate the same I-uniformity in fuzzy METRIC SPACES.

We introduce the idea of SJS-METRIC SPACES which is a gener-alization of S-METRIC SPACES. Next we study the properties of SJS-METRIC SPACES and prove several theorems. We also deal with abstract SJS-topological SPACES induced by SJS-METRIC and obtain several classical results including Cantor's intersection theorem in this setting.