On the Almost Periodic Solutions of a Class of Integro-Differential-Difference Equations

Abstract

It is well known that if the derivative of an a.p. function is uniformly continuous, then this derivative is a.p. Hence an immediate consequence of (a) is that if, for a solution f (x) of (1), f (x), f '(x), **, f (r)(x) are bounded and uniformly continuous, then f (x), f '(x), *_* *, f (r)(x) are all a.p. This last result has been proved by Bochner [2] and [3] under the additional assumption that K(x) 0 (and that the = 6, are independent of p).