Convex functions and the rolling circle criterion

Convex functions and the rolling circle criterion

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 fo...

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Bibliographic Details
Main Authors: V. Srinivas, O. P. Juneja, G. P. Kapoor
Format: Article
Language:English
Published: Hindawi Limited 1995-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
univalent functions
convex functions
curvature
subordination
distortion theorems
growth theorems.
Online Access:http://dx.doi.org/10.1155/S0161171295001025
Description
Summary: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.
ISSN:0161-1712
1687-0425

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