2020/05/27 by Sumit Som, Adrian Petruşel, Som, Sumit +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.2005.13345
openalex publication_date 2020/05/27 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In cite[ , An, V.T., Tuyen, Q.L. and Dung, V.N., Stone-type theorem on\nb-metric spaces and applications, Topology Appl. 185-186 (2015), 50-64.]an,\nAn et al. had provided a sufficient condition for b-metric spaces to be\nmetrizable. However, their proof of metrizability relied on an assumption that\nthe distance function is continuous in one variable. In this short note, we\nimprove upon this result in a more simplified way without considering any\nassumption on the distance function. Moreover, we provide two shorter proofs of\nthe metrizability of \F-metric spaces recently introduced by Jleli\nand Samet in cite[ , Jleli, M. and Samet, B., On a new generalization of\nmetric spaces, J. Fixed Point Theory Appl. (2018) 20:128]JS1. Lastly, in this\nshort note, we give an alternative proof of the metrizability of\n\θ-metric spaces introduced by Khojasteh et al. in cite[ , Khojasteh,\nF., Karapinar, E. and Radenovic, S., \θ-metric space: A Generalization,\nMath. Probl. Eng. Volume 2013, Article 504609, 7 pages]ks.\n