Geometric Properties of Partial Sums of Univalent Functions

The nth partial sum of an analytic function f(z) = z+ k=2 akz k is the polynomial fn(z): = z+ ∑n k=2 akz k. A survey of the univalence and other geometric properties of the nth partial sum of univalent functions as well as other related functions including those of starlike, convex and close-to-convex functions are presented. 1