Some remarks concerning D∗-metric spaces

Abstract

In [S. Sedghi, N. Shobe, H. Y. Zhou, Fixed Point Theory Appl., 2007 (2007), 13 pages], Sedghi et al. introduced the notion of D∗ -metric space and in [S. Sedghi, N. Shobe, A. Aliouche, Mat. Vesnik, 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.