Radius problems for a subclass of close-to-convex univalent functions

Let P[A,B], −1≤B<A≤1, be the class of functions p such that p(z) is subordinate to 1+Az1+Bz. A function f, analytic in the unit disk E is said to belong to the class Kβ*[A,B] if, and only if, there exists a function g with zg′(z)g(z)∈P[A,B] such that Re(zf′(z))′g′(z)>β, 0≤β<1 and z∈E. The f...

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Main Author:	Khalida Inayat Noor
Format:	Article
Language:	English
Published:	Hindawi Limited 1992-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	close-to-convex starlike univalent convex radius of convexity.
Online Access:	http://dx.doi.org/10.1155/S0161171292000930

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spelling	doaj-8230cff7196241c2bd6d47f25331a11e2020-11-25T00:30:05ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115471972610.1155/S0161171292000930Radius problems for a subclass of close-to-convex univalent functionsKhalida Inayat Noor0Mathematics Department, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaLet P[A,B], −1≤B<A≤1, be the class of functions p such that p(z) is subordinate to 1+Az1+Bz. A function f, analytic in the unit disk E is said to belong to the class Kβ*[A,B] if, and only if, there exists a function g with zg′(z)g(z)∈P[A,B] such that Re(zf′(z))′g′(z)>β, 0≤β<1 and z∈E. The functions in this class are close-to-convex and hence univalent. We study its relationship with some of the other subclasses of univalent functions. Some radius problems are also solved.http://dx.doi.org/10.1155/S0161171292000930close-to-convexstarlike univalentconvexradius of convexity.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Khalida Inayat Noor
spellingShingle	Khalida Inayat Noor Radius problems for a subclass of close-to-convex univalent functions International Journal of Mathematics and Mathematical Sciences close-to-convex starlike univalent convex radius of convexity.
author_facet	Khalida Inayat Noor
author_sort	Khalida Inayat Noor
title	Radius problems for a subclass of close-to-convex univalent functions
title_short	Radius problems for a subclass of close-to-convex univalent functions
title_full	Radius problems for a subclass of close-to-convex univalent functions
title_fullStr	Radius problems for a subclass of close-to-convex univalent functions
title_full_unstemmed	Radius problems for a subclass of close-to-convex univalent functions
title_sort	radius problems for a subclass of close-to-convex univalent functions
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1992-01-01
description	Let P[A,B], −1≤B<A≤1, be the class of functions p such that p(z) is subordinate to 1+Az1+Bz. A function f, analytic in the unit disk E is said to belong to the class Kβ*[A,B] if, and only if, there exists a function g with zg′(z)g(z)∈P[A,B] such that Re(zf′(z))′g′(z)>β, 0≤β<1 and z∈E. The functions in this class are close-to-convex and hence univalent. We study its relationship with some of the other subclasses of univalent functions. Some radius problems are also solved.
topic	close-to-convex starlike univalent convex radius of convexity.
url	http://dx.doi.org/10.1155/S0161171292000930
work_keys_str_mv	AT khalidainayatnoor radiusproblemsforasubclassofclosetoconvexunivalentfunctions
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Radius problems for a subclass of close-to-convex univalent functions

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