A Certain Subclass of Multivalent Functions Involving Higher-Order Derivatives

Abstract

In this paper we introduce and study a new class of analytic and $p$-valent
functions involving higher-order derivatives. For this $p$-valent function class, we
derive several interesting properties including (for example) coefficient
inequalities, distortion theorems, extreme points, and the radii of
close-to-convexity, starlikeness and convexity. Several
applications involving an integral operator are also considered.
Finally, we obtain some results for the modified Hadamard product of the functions
belonging to the $p$-valent function class
which is introduced here.