International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 799-811
doi:10.1155/S0161171295001025
Convex functions and the rolling circle criterion
V. Srinivas
, O.P. Juneja
and G.P. Kapoor
Department of Mathematics, Indian Institute of Technology, Kanpur 208016, India
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.