半群和群上的完全不变模糊度量

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Journal of Applied Analysis and Computation Pub Date : 2021-01-01 DOI:10.11948/20190394

Jin-Ji Tu, L. Xie

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引用次数: 4

摘要

本文研究了不变模糊度量群和完全模糊度量半群(在Kramosil和Michael意义上)的Raǐkov补齐性。我们证明:(1)如果(G, M，∗)是一个模糊度量群使得(M，∗)是不变的，那么(G， τ M)的Raǐkov补全ϱG是一个模糊度量群(ϱG, f M，∗)使得(f M，∗)在ϱG上是不变的并且f M | G × G ×[0，∞)= M;(2)如果(G, M，∗)是一个模糊度量半群，使得(M，∗)是不变的，则(G, M，∗)的模糊度量补全(G, f M，∗)是一个模糊度量半群并且(f M，∗)是不变的。

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COMPLETE INVARIANT FUZZY METRICS ON SEMIGROUPS AND GROUPS

In this paper, we study the Raǐkov completion of invariant fuzzy metric groups and complete fuzzy metric semigroups (in the sense of Kramosil and Michael). We establish that: (1) if ( G, M, ∗ ) is a fuzzy metric group such that ( M, ∗ ) is invariant, then the Raǐkov completion ϱG of ( G, τ M ) is a fuzzy metric group ( ϱG, f M, ∗ ) such that ( f M, ∗ ) is invariant on ϱG and f M | G × G × [0 , ∞ ) = M ; (2) if ( G, M, ∗ ) is a fuzzy metric semigroup such that ( M, ∗ ) is invariant, then a fuzzy metric completion ( e G, f M, ∗ ) of ( G, M, ∗ ) is a fuzzy metric semigroup and ( f M, ∗ ) is invariant.

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来源期刊

Journal of Applied Analysis and Computation MATHEMATICS, APPLIED-

CiteScore

2.30

自引率

9.10%

发文量

期刊介绍： The Journal of Applied Analysis and Computation (JAAC) is aimed to publish original research papers and survey articles on the theory, scientific computation and application of nonlinear analysis, differential equations and dynamical systems including interdisciplinary research topics on dynamics of mathematical models arising from major areas of science and engineering. The journal is published quarterly in February, April, June, August, October and December by Shanghai Normal University and Wilmington Scientific Publisher, and issued by Shanghai Normal University.