  Let $A(k)u(k)=f(k) (1)$ be an operator equation, $X$ and $Y$ are Banach
spaces, $k\in\Delta\subset\C$ is a parameter, $A(k):X\to Y$ is a map, possibly
nonlinear. Sufficient conditions are given for continuity of $u(k)$ with
respect to $k$. Necessary and sufficient conditions are given for the
continuity of $u(k)$ with respect to $k$ in the case of linear operators
$A(k)$.
