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

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spelling	doaj-414d8dc7c5954b01af0c7b1d5e584be42020-11-24T22:57:39ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118479981110.1155/S0161171295001025Convex functions and the rolling circle criterionV. Srinivas0O. P. Juneja1G. P. Kapoor2Department of Mathematics, Indian Institute of Technology, Kanpur 208016, IndiaDepartment of Mathematics, Indian Institute of Technology, Kanpur 208016, IndiaDepartment of Mathematics, Indian Institute of Technology, Kanpur 208016, IndiaGiven 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.http://dx.doi.org/10.1155/S0161171295001025univalent functionsconvex functions curvaturesubordinationdistortion theoremsgrowth theorems.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	V. Srinivas O. P. Juneja G. P. Kapoor
spellingShingle	V. Srinivas O. P. Juneja G. P. Kapoor Convex functions and the rolling circle criterion International Journal of Mathematics and Mathematical Sciences univalent functions convex functions curvature subordination distortion theorems growth theorems.
author_facet	V. Srinivas O. P. Juneja G. P. Kapoor
author_sort	V. Srinivas
title	Convex functions and the rolling circle criterion
title_short	Convex functions and the rolling circle criterion
title_full	Convex functions and the rolling circle criterion
title_fullStr	Convex functions and the rolling circle criterion
title_full_unstemmed	Convex functions and the rolling circle criterion
title_sort	convex functions and the rolling circle criterion
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1995-01-01
description	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.
topic	univalent functions convex functions curvature subordination distortion theorems growth theorems.
url	http://dx.doi.org/10.1155/S0161171295001025
work_keys_str_mv	AT vsrinivas convexfunctionsandtherollingcirclecriterion AT opjuneja convexfunctionsandtherollingcirclecriterion AT gpkapoor convexfunctionsandtherollingcirclecriterion
_version_	1725649872746446848

Convex functions and the rolling circle criterion

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