Journal
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
Volume 97, Issue 3, Pages 435-445Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0004972717001125
Keywords
univalent functions; convex functions; Caratheodory functions; Hankel determinant
Categories
Funding
- National Research Foundation of Korea (NRF) - Korea government (Ministry of Science, ICT and Future Planning) [NRF-2017R1C1B5076778]
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We prove the sharp inequality vertical bar H-3,H-1(f)vertical bar <= 4/135 for convex functions, that is, for analytic functions f with a(n) := f((n))(0)/n!, n epsilon N, such that Re{1 + z f(z)/f'(z)} > 0 for z is an element of D : = {z is an element of C : vertical bar z vertical bar < 1 }, where H-3,H-1(f) is the third Hankel determinant H-3,H-1(f) := vertical bar a(1) a(2) a(3) a(2) a(3) a(4) a(3) a(4) a(5)vertical bar .
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