Vol. 20(2019) No. 1

 

 

  Remarks on Frink's metrization technique and applications
 
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Fixed Point Theory, Volume 20, No. 1, 2019, 157-176, February 1st, 2019

DOI: 10.24193/fpt-ro.2019.1.09

Authors: Nguyen Van Dung, Tran Van An and Vo Thi Le Hang

Abstract: In this paper, we give a simple counterexample to show again the limits of Frink’s construction [17, page 134] and then use Frink’s metrization technique to answer two conjectures posed by Berinde and Choban [5], and to calculate corresponding metrics induced by some b-metrics known in the literature. We also use that technique to prove a metrization theorem for 2-generalized metric spaces, and to deduce the Banach contraction principle in b-metric spaces and 2-generalized metric spaces from that in metric spaces.

Key Words and Phrases: Metrization, quasi-metric, b-metric, 2-generalized metric, fixed point.

2010 Mathematics Subject Classification: 54E35, 54H25, 47H10.

Published on-line: February 1st, 2019.

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