Uniformly Convex and Uniformly Starlike Functions

Abstract

A normalized univalent function is uniformly convex if it maps every circular arc contained in the open unit disk with center in it into a convex curve. This article surveys recent results on the class of uniformly convex functions and on an analogous class of uniformly starlike functions.

Cited by in corpus (4)

• On the radius constants for classes of analytic functions
• Coefficient Inequalities for Starlikeness and Convexity
• Geometric Properties of Partial Sums of Univalent Functions
• Radii of Starlikeness and Convexity of Analytic Functions Satisfying Certain Coefficient Inequalities