The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions of Order 1/2

摘要

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.