Stability of normal regions for linear homogeneous functional equations
The solution of the functional equation (1) \(\phi [f(x)]=g(x)\phi (x)\) is known to depend on an arbitrary function \(\phi_ 0(x)\) if certain simple conditions on f and g are satisfied. Starting from the notion of set stability for difference equations, introduced by \textit{G. A. Shanholt} [Int. J. Control, I. Ser. 19, 309-314 (1974; Zbl 0291.93036)], the author defines stability in the context of (1) and proceeds to give a number of results on stability, in particular also about continuous dependence on initial conditions.
scientific article; zbMATH DE number 4086212