Uniformly Convex and Uniformly Starlike Functions
R.M. Ali, and V. Ravichandran
TL;DR
This paper surveys recent advances in the study of uniformly convex and uniformly starlike functions, focusing on their geometric properties and classifications within complex analysis.
Contribution
It provides a comprehensive overview of recent results concerning the properties and classifications of uniformly convex and starlike functions.
Findings
Characterization of uniformly convex functions
Properties of uniformly starlike functions
Connections between convexity and starlikeness in univalent 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.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Algebraic and Geometric Analysis