Journal
COMPLEX ANALYSIS AND OPERATOR THEORY
Volume 13, Issue 5, Pages 2231-2238Publisher
SPRINGER BASEL AG
DOI: 10.1007/s11785-018-0819-0
Keywords
Starlike functions of order 1/2; Caratheodory functions; Hankel determinant; Coefficients
Categories
Funding
- National Research Foundation of Korea (NRF) - Korea government (Ministry of Science, ICT and Future Planning) [NRF-2017R1C1B5076778]
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In the present paper, we proved the sharp inequality | H3,1( f)| = 1/ 9 for analytic functions f with an := f ( n)( 0)/ n!, n. N, a1 := 1, such that Re z f ( z) f ( z) > 1 2, z. D := {z. C : | z| < 1}, where H3,1( f) := a1 a2 a3 a2 a3 a4 a3 a4 a5 is the third Hankel determinant.
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