Abstract
In this paper we introduce some new subclasses of the
-valent analytic functions with higher-order derivatives that generalize some related subclasses of starlike and convex functions of a positive order. We found the order of (
)-valent starlikeness and convexity for the products of functions that belong to these classes. The order of (
)-valent starlikeness and convexity of certain integral operators for the product of functions of these classes were also obtained.