论文标题
一些关于某些众所周知的广义度量样结构的衡量性的评论
Some remarks on the metrizability of some well known generalized metric-like structures
论文作者
论文摘要
在\ cite [\，an，v.t.，tuyen，q.l。和Dung，V.N.，$ b $ mmetric空间和应用的Stone-Type定理，Toupology Appl。 185-186（2015），50-64。] {an}，An等。已经为$ b $ - 美度空间提供了足够的条件。但是，它们的衡量性证明取决于一个假设，即距离函数在一个变量中是连续的。在此简短说明中，我们以更简化的方式改进了这种结果，而无需考虑距离函数的任何假设。此外，我们提供了两个较短的证据，证明了$ \ Mathcal {f} $ - 公制空间最近由Jleli和Samet在\ cite [\，Jleli，M。和Samet，B。中引入的，这是对度量的新概括的度量标准概括，J。固定点理论应用。 （2018）20：128] {JS1}。最后，在简短的说明中，我们给出了Khojasteh等人引入的$θ$ mmetric空间的METRINASINIDE的替代证明。在\ cite [\，khojasteh，F.，Karapinar，E。和Radenovic，S.，$θ$ - metric Space：概括，数学。 Probl。工程。第2013卷，第504609条，第7页] {ks}。
In \cite[\, An, V.T., Tuyen, Q.L. and Dung, V.N., Stone-type theorem on $b$-metric spaces and applications, Topology Appl. 185-186 (2015), 50-64.]{an}, An et al. had provided a sufficient condition for $b$-metric spaces to be metrizable. However, their proof of metrizability relied on an assumption that the distance function is continuous in one variable. In this short note, we improve upon this result in a more simplified way without considering any assumption on the distance function. Moreover, we provide two shorter proofs of the metrizability of $\mathcal{F}$-metric spaces recently introduced by Jleli and Samet in \cite[\, Jleli, M. and Samet, B., On a new generalization of metric spaces, J. Fixed Point Theory Appl. (2018) 20:128]{JS1}. Lastly, in this short note, we give an alternative proof of the metrizability of $θ$-metric spaces introduced by Khojasteh et al. in \cite[\, Khojasteh, F., Karapinar, E. and Radenovic, S., $θ$-metric space: A Generalization, Math. Probl. Eng. Volume 2013, Article 504609, 7 pages]{ks}.
