Convex functions and the rolling circle criterion

Abstract

Given 0≤R1≤R2≤∞, CVG(R1,R2) denotes the class of normalized convex functions f in the unit disc U, for which ∂f(U) satisfies a Blaschke Rolling Circles Criterion with radii R1 and R2. Necessary and sufficient conditions for R1=R2, growth and distortion theorems for CVG(R1,R2) and rotation theorem for the class of convex functions of bounded type, are found.

Keywords

• univalent functions
• convex functions
• curvature
• subordination
• distortion theorems
• growth theorems.