Sufficient Conditions for Janowski Starlikeness

Sufficient Conditions for Janowski Starlikeness

Let A,B,D,E∈[−1,1] and let p(z) be an analytic function defined on the open unit disk, p(0)=1. Conditions on A, B, D, and E are determined so that 1+βzp'(z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz). Similar results are obtained by considering the ex...

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Main Authors: Rosihan M. Ali, V. Ravichandran, N. Seenivasagan
Format: Article
Language:English
Published: Hindawi Limited 2007-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2007/62925
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spelling doaj-58d207c28c81403e9ac9a660a7ca3ab82020-11-25T02:28:08ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/6292562925Sufficient Conditions for Janowski StarlikenessRosihan M. Ali0V. Ravichandran1N. Seenivasagan2School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800 USM, MalaysiaSchool of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800 USM, MalaysiaSchool of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800 USM, MalaysiaLet A,B,D,E∈[−1,1] and let p(z) be an analytic function defined on the open unit disk, p(0)=1. Conditions on A, B, D, and E are determined so that 1+βzp'(z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz). Similar results are obtained by considering the expressions 1+β(zp'(z)/p(z)) and 1+β(zp'(z)/p2(z)). These results are then applied to obtain sufficient conditions for analytic functions to be Janowski starlike.http://dx.doi.org/10.1155/2007/62925
collection DOAJ
language English
format Article
sources DOAJ
author Rosihan M. Ali
V. Ravichandran
N. Seenivasagan
spellingShingle Rosihan M. Ali
V. Ravichandran
N. Seenivasagan
Sufficient Conditions for Janowski Starlikeness
International Journal of Mathematics and Mathematical Sciences
author_facet Rosihan M. Ali
V. Ravichandran
N. Seenivasagan
author_sort Rosihan M. Ali
title Sufficient Conditions for Janowski Starlikeness
title_short Sufficient Conditions for Janowski Starlikeness
title_full Sufficient Conditions for Janowski Starlikeness
title_fullStr Sufficient Conditions for Janowski Starlikeness
title_full_unstemmed Sufficient Conditions for Janowski Starlikeness
title_sort sufficient conditions for janowski starlikeness
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2007-01-01
description Let A,B,D,E∈[−1,1] and let p(z) be an analytic function defined on the open unit disk, p(0)=1. Conditions on A, B, D, and E are determined so that 1+βzp'(z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz). Similar results are obtained by considering the expressions 1+β(zp'(z)/p(z)) and 1+β(zp'(z)/p2(z)). These results are then applied to obtain sufficient conditions for analytic functions to be Janowski starlike.
url http://dx.doi.org/10.1155/2007/62925
work_keys_str_mv AT rosihanmali sufficientconditionsforjanowskistarlikeness
AT vravichandran sufficientconditionsforjanowskistarlikeness
AT nseenivasagan sufficientconditionsforjanowskistarlikeness
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