  The main aim of this note is to point out by means of counter-examples that
some arguments of the proofs of two theorems about a "half variational
principle" for multivalued maps, formulated recently by Vivas and Sirvent
[Metric entropy for set-valued maps, Discrete Contin. Dyn. Syst. Ser. B, 27
(2022), pp. 6589-6604], are false and that our corrected versions require
rather restrictive additional assumptions. Nevertheless, we will be able to
establish the full variational principle for a special subclass of multivalued
lower semicontinuous maps with convex compact values on a compact subset of a
Banach space.
