International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 799-811

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

Received 31 May 1991; Revised 7 September 1993

Copyright © 1995 V. Srinivas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Given 0R1R2, 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.