The investigation of k-fuzzy metric spaces with the first contraction principle in such spaces

被引:4
作者
Gopal, Dhananjay [1 ]
Sintunavarat, Wutiphol [2 ]
Ranadive, Abhay S. [1 ]
Shukla, Satish [3 ]
机构
[1] Guru Ghasidas Vishwavidyalya Bilaspur, Dept Math, Bilaspur 495009, Chhattisgarh, India
[2] Thammasat Univ, Fac Sci & Technol, Dept Math & Stat, Rangsit Ctr, Khlong Luang 12120, Pathum Thani, Thailand
[3] Shri Vaishnav Vidyapeeth Vishwavidyalaya, Shri Vaishnav Inst Sci, Dept Math, Indore 453331, Madhya Pradesh, India
关键词
k-fuzzy metric spaces; Hausdorff spaces; Contractions; Fixed points;
D O I
10.1007/s00500-023-07946-y
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
This paper introduces the notion of k-fuzzy metric spaces, which generalizes and extends the concept of fuzzy metric spaces due to George and Veeramani in [A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395-399.] for the fuzzy sets involving more than one (k) parameters. It is shown that the topology generated by the k-fuzzy metric is first countable, and the k-fuzzy metric space is Hausdorff. Finally, we prove a fixed point theorem, which generalizes and extends the results of Grabiec [M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389.] into k-fuzzy metric spaces.
引用
收藏
页码:11081 / 11089
页数:9
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