The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions with Real Coefficients

Oh Sang Kwon and Young Jae Sim
Additional contact information
Oh Sang Kwon: Department of Mathematics, Kyungsung University, Busan 48434, Korea
Young Jae Sim: Department of Mathematics, Kyungsung University, Busan 48434, Korea

Mathematics, 2019, vol. 7, issue 8, 1-14

Abstract: Let SR * be the class of starlike functions with real coefficients, i.e., the class of analytic functions f which satisfy the condition f ( 0 ) = 0 = f ′ ( 0 ) − 1 , Re { z f ′ ( z ) / f ( z ) } > 0 , for z ∈ D : = { z ∈ C : | z | < 1 } and a n : = f ( n ) ( 0 ) / n ! is real for all n ∈ N . In the present paper, it is obtained that the sharp inequalities − 4 / 9 ≤ H 3 , 1 ( f ) ≤ 3 / 9 hold for f ∈ SR * , where H 3 , 1 ( f ) is the third Hankel determinant of order 3 defined by H 3 , 1 ( f ) = a 3 ( a 2 a 4 − a 3 2 ) − a 4 ( a 4 − a 2 a 3 ) + a 5 ( a 3 − a 2 2 ) .

Keywords: starlike functions; hankel determinant; carathéodory functions; schwarz functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/8/721/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/8/721/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:8:p:721-:d:255880

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().