Some remarks concerning D∗-metric spaces

Abstract

In [S. Sedghi, N. Shobe, H. Y. Zhou, Fixed Point Theory Appl., {\bf 2007} (2007), 13 pages], Sedghi et al. introduced the notion of \(D^{*}\)-metric space and in [S. Sedghi, N. Shobe, A. Aliouche, Mat. Vesnik, \(\bf 64\) (2012), 258--266] the authors claimed that every \(G\)-metric space is \(D^{*}\)-metric. In this short paper we present examples to show that \(D^{*}\)-metric need not be \(G\)-metric as well as the \(G\)-metric need not be \(D^{*}\)-metric.

Topics & Concepts