Geometric Properties of Partial Sums of Univalent Functions

Abstract

The $n$th partial sum of an analytic function $f(z)=z+{\sum }_{k=2}^{\infty }{a}_k{z}^k$ is the polynomial $f_n(z):=z+{\sum }_{k=2}^n{a}_k{z}^k$. A survey of the univalence and other geometric properties of the $n$th partial sum of univalent functions as well as other related functions including those of starlike, convex and close-to-convex functions are presented.

References in corpus (1)

• Radius of Close-to-convexity of Harmonic Functions