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.