On the continuity of the Volterra variational derivative (Q580659)

The author gives a sufficient condition for the continuity of the Volterra variational derivative of a nonlinear functional defined on some space of continuous functions, with respect to a fixed function. As a corollary it is shown that the variational derivative of a linear functional is always continuous (on the set of those points for which this derivative exists). This corollary is a generalization of Theorem 2 in the paper by \textit{E. P. Hamilton} and \textit{M. Z. Nashed} [J. Funct. Anal. 49, 128-144 (1982; Zbl 0498.46030)].