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
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.
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页数:7
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