Integral means of certain class of analytic functions

In this paper we discuss the following class of functions Sλ(α,β)={f(z):|f(z)g(z)−1|<β|λf(z)g(z)+1|,z∈D} where 0≤λ≤1,0<β≤1,0≤α<1, and f(z)=z+∑n=2∞anzn is analytic in D={z:|z|<1}, g(z) is a starlike function of order α. A subordination about this class is obtained, the integral means of...

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Main Author:	Gao Chunyi
Format:	Article
Language:	English
Published:	Hindawi Limited 1993-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	analytic function subordination integral mean distortion coefficient inequality.
Online Access:	http://dx.doi.org/10.1155/S0161171293000572

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record_format	Article
spelling	doaj-8b757a1ed96340469ca892e68fe83ffd2020-11-24T21:19:52ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116345946410.1155/S0161171293000572Integral means of certain class of analytic functionsGao Chunyi0Department of Mathematics, Changsha Communications Institute, Hunan, Changsha 410076, ChinaIn this paper we discuss the following class of functions Sλ(α,β)={f(z):\|f(z)g(z)−1\|<β\|λf(z)g(z)+1\|,z∈D} where 0≤λ≤1,0<β≤1,0≤α<1, and f(z)=z+∑n=2∞anzn is analytic in D={z:\|z\|<1}, g(z) is a starlike function of order α. A subordination about this class is obtained, the integral means of functions in Sλ(α,β) and some extremal properties are studied.http://dx.doi.org/10.1155/S0161171293000572analytic functionsubordinationintegral meandistortion coefficient inequality.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Gao Chunyi
spellingShingle	Gao Chunyi Integral means of certain class of analytic functions International Journal of Mathematics and Mathematical Sciences analytic function subordination integral mean distortion coefficient inequality.
author_facet	Gao Chunyi
author_sort	Gao Chunyi
title	Integral means of certain class of analytic functions
title_short	Integral means of certain class of analytic functions
title_full	Integral means of certain class of analytic functions
title_fullStr	Integral means of certain class of analytic functions
title_full_unstemmed	Integral means of certain class of analytic functions
title_sort	integral means of certain class of analytic functions
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1993-01-01
description	In this paper we discuss the following class of functions Sλ(α,β)={f(z):\|f(z)g(z)−1\|<β\|λf(z)g(z)+1\|,z∈D} where 0≤λ≤1,0<β≤1,0≤α<1, and f(z)=z+∑n=2∞anzn is analytic in D={z:\|z\|<1}, g(z) is a starlike function of order α. A subordination about this class is obtained, the integral means of functions in Sλ(α,β) and some extremal properties are studied.
topic	analytic function subordination integral mean distortion coefficient inequality.
url	http://dx.doi.org/10.1155/S0161171293000572
work_keys_str_mv	AT gaochunyi integralmeansofcertainclassofanalyticfunctions
_version_	1726004803795943424

Integral means of certain class of analytic functions

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