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Silverman (4) was defined the class of univalent functions f(z )= z+ ∞ ∑ k=2 akz k for which arg(ak) prescribed in such way that f(z) is univalent if and only if f(z) is starlike. In this paper we introduce the subclass of p-valent functions with varying arguments, especially p-valent starlike functions and pvalent convex functions, moreover we give some interesting properties of functions in these classes, including coefficients estimates, distortion theorems and extreme functions. Mathematics subject classification (2010): 30C45. Keywords and phrases: Analytic, varying arguments, extreme points.

Multivalent functions with varying arguments