A class of bounded starlike functions

We consider functions f(z)=z+… that are analytic in the unit disk and satisfy there the inequality Re(f′(z)+zf″(z))>α, α<1. We find extreme points and then determine sharp lower bounds on Ref′(z) and Re(f(z)/z). Sharp results for the sequence of partial sums are also found.

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Bibliographic Details
Main Author: Herb Silverman
Format: Article
Language:English
Published: Wiley 1994-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171294000360
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author Herb Silverman
author_facet Herb Silverman
author_sort Herb Silverman
collection DOAJ
description We consider functions f(z)=z+… that are analytic in the unit disk and satisfy there the inequality Re(f′(z)+zf″(z))>α, α<1. We find extreme points and then determine sharp lower bounds on Ref′(z) and Re(f(z)/z). Sharp results for the sequence of partial sums are also found.
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1687-0425
language English
publishDate 1994-01-01
publisher Wiley
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-e3a826dce2b74ee08b49eacd7b66cbeb2025-08-20T02:21:24ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117224925210.1155/S0161171294000360A class of bounded starlike functionsHerb Silverman0Department of Mathematics, University of Charleston, Charleston 29424, SC, USAWe consider functions f(z)=z+… that are analytic in the unit disk and satisfy there the inequality Re(f′(z)+zf″(z))>α, α<1. We find extreme points and then determine sharp lower bounds on Ref′(z) and Re(f(z)/z). Sharp results for the sequence of partial sums are also found.http://dx.doi.org/10.1155/S0161171294000360univalentstarlike.
spellingShingle Herb Silverman
A class of bounded starlike functions
International Journal of Mathematics and Mathematical Sciences
univalent
starlike.
title A class of bounded starlike functions
title_full A class of bounded starlike functions
title_fullStr A class of bounded starlike functions
title_full_unstemmed A class of bounded starlike functions
title_short A class of bounded starlike functions
title_sort class of bounded starlike functions
topic univalent
starlike.
url http://dx.doi.org/10.1155/S0161171294000360
work_keys_str_mv AT herbsilverman aclassofboundedstarlikefunctions
AT herbsilverman classofboundedstarlikefunctions