2019/09/17 by Sumit Som, Som, Sumit
Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.1909.07693
openalex publication_date 2019/09/17 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
In [An, V.T., Tuyen, Q.L., Dung, V.N., Stone-type theorem on b-metric spaces and applications, Topology Appl. 185-186 (2015) 50-64], Tran Van An et al. provide a sufficient condition for b-metric space to be metrizable. They proved the metrizability by assuming that the distance function is continuous in one variable. The main purpose of this manuscript is to provide a direct short proof of the metrizability of b-metric space introduced by Khamsi and Hussain in \cite[ Khamsi, M.A and Hussain, N., KKM mappings in metric type spaces, Nonlinear Anal. 73 (9) (2010) 3123-3129]kh via Chittenden's metrization theorem without any assumption on the distance function. Further in this short note, we prove the metrizability of θ-metric space introduced by Khojasteh et al. in [Khojasteh, F., Karapinar, E., Radenovic, S., θ-metric space: A Generalization, Mathematical problems in Engineering, Volume 2013, Article 504609, 7 pages].