In this paper we introduce some subclasses of analytic functions with varying argument of coeffcients. These classes are defined in terms of the Hadamard product and generalize the well-known classes of uniformly convex functions. We investigate the coeffcients estimates, distortion properties, radii of starlikeness and convexity for defined classes of functions.
Let H = H(U) be the class of all functions which are holomorphic in the unit disc U = {z : \z\ < 1}. Let P(n) denotes the class of all functions p(z) = 1+piz+... is an element H, such thatp(pz) -< (1+zn/(1-zn), where -< denotes subordination. With the class P(n) we connect the subclass S*(n) of starlike functions in the following way. A function f(z) = z + a2z + ... belongs to S* (n) if and only if zf'(z)/f(z) is an element of P(n). In this note we give the estimations of some coefficients in the classes P(n) and S*(n) and we find the radius of convexity of the class S*(n).
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