Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results

被引：8

作者：

Romaguera, Salvador ^{[1
]}

Tirado, Pedro ^{[1
]}

机构：

[1] Univ Politecn Valencia, IUMPA, E-46022 Valencia, Spain

来源：

MATHEMATICS | 2020年 / 8卷 / 02期

关键词：

fuzzy metric space; complete; fixed point; hicks contraction; 54H25; 54A40; 54E50; 54E70; t; CONTRACTIONS; PRINCIPLE; MAPPINGS; THEOREMS;

D O I：

10.3390/math8020273

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see "Am. Math. Month. 1967, 74, 436-437") that a metric space is complete if and only if any Banach contraction on any of its closed subsets has a fixed point. We apply our main result to deduce that a well-known fixed point theorem due to D. Mihet (see "Fixed Point Theory 2005, 6, 71-78") also allows us to characterize the fuzzy metric completeness.

引用

页数：7