  In 1968, H. Brezis introduced a notion of operator pseudomonotonicity which
provides a unified approach to monotone and nonmonotone variational
inequalities (VIs). A closely related notion is that of Ky-Fan hemicontinuity,
a continuity property which arises if the famous Ky-Fan minimax inequality is
applied to the VI framework. It is clear from the corresponding definitions
that Ky-Fan hemicontinuity implies Brezis pseudomonotonicity, but quite
surprisingly, a recent publication by Sadeqi and Paydar (J. Optim. Theory
Appl., 165(2):344-358, 2015) claims the equivalence of the two properties. The
purpose of the present note is to show that this equivalence is false; this is
achieved by providing a concrete example of a nonlinear operator which is
Brezis pseudomonotone but not Ky--Fan hemicontinuous.
