a b s t r a c tThe main object of this work is to extend the univalent condition for a family of integral operators. Several other closely-related results are also considered. A number of known univalent conditions would follow upon specializing the parameters involved in our main result.

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 closeto-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.

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