Some Notes on the paper "The Equivalence of Cone Metric Spaces and Metric Spaces"

TL;DR

This paper demonstrates the equivalence of cone metric spaces and metric spaces as established by Feng, Mao, and Du, and provides examples using the metrics to illustrate their practical similarities.

Contribution

It proves the equivalence of cone metric spaces and metric spaces as previously claimed, and includes concrete examples to illustrate this equivalence.

Findings

Metrics obtained by Feng and Mao are equivalent to standard metrics.

Metrics obtained by Du are also equivalent to standard metrics.

Examples confirm the practical similarity of these metrics.

Abstract

In this paper we shall show that the metrics are equivalent which obtained by Feng and Mao in [[1], Y. Feng and W. Mao, Equivalence of Cone Metric spaces and Metric Spaces, Fixed Point Theory, 11(2)(2010), 259-264.] and Du in [[2], Wei-Shih Du, A Note on Cone Metric Fixed Point Theory and its equivalence, Nonlinear Analysis, 72 2259-2261 (2010)]. Also in the sequel we calculate some examples by one of the metrics.