The types of mapping to which the title refers were defined by

*T. Husain* and

*A. Latif* [Math. Jap. 33, No.3, 385-391 (1988;

Zbl 0667.47028)] and by

*T. Husain* and

*E. Tarafdar* [Yokohama Math. J. 28, 1-6 (1980;

Zbl 0456.47047)]. As the author points out, it is immediate from the definition of “weakly non-expansive” that it implies “non-expansive” in the usual sense with respect to the Hausdorff metric and hence that the work of the above mentioned authors dealing with this concept is subsumed under earlier work on non-expansive maps by

*Lami Dozo*,

*Lim* and

*Kirk*. The paper also gives simple examples to show that there are

${}^{*}$non-expansive maps which are not non- expansive and vice versa (correcting a further statement of Husain and Latif). Finally, the paper contains a fixed-point theorem for

${}^{*}non$-expansive maps.