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In this paper we introduce some new subclasses of the  p -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 ( p , q )-valent starlikeness and convexity for the products of functions that belong to these classes. The order of ( p , q )-valent starlikeness and convexity of certain integral operators for the product of functions of these classes were also obtained.

Starlikeness and convexity of the product of certain multivalent functions with higher-order derivatives