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: Wiley 1993-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171293000572
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author Gao Chunyi
author_facet Gao Chunyi
author_sort Gao Chunyi
collection DOAJ
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.
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institution Kabale University
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publishDate 1993-01-01
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-8b757a1ed96340469ca892e68fe83ffd2025-02-03T05:44:16ZengWileyInternational 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.
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.
title 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_short Integral means of certain class of analytic functions
title_sort integral means of certain class of analytic functions
topic analytic function
subordination
integral mean
distortion
coefficient inequality.
url http://dx.doi.org/10.1155/S0161171293000572
work_keys_str_mv AT gaochunyi integralmeansofcertainclassofanalyticfunctions