Partial sums of certain univalent functions

Abstract

The partial sums f3(z) of some extermal functions for various classes S∗, K and R of starlike functions, convex functions and functions with positive real part in the open unit disk U, respectively, are discussed. In general, the partial sums can not preserve the same character as the initial functions. The object of the present paper is to discuss the radius problems for partial sums of some extremal functions for the classes S∗, K and R.