Abstract
Abstract In this paper, we prove the sharp inequality | H 3 , 1 ( f ) | ≤ 4 / 9 \lvert H_{3,1}(f)\rvert\leq 4/9 for starlike functions 𝑓, where H 3 , 1 ( f ) H_{3,1}(f) is the third Hankel determinant, thus solving a long-standing problem.
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