The sharp bound of the third Hankel determinant for starlike functions

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2022-07-30 DOI:10.1515/forum-2021-0308

B. Kowalczyk, A. Lecko, D. K. Thomas

引用次数: 10

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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星形函数的第三汉克尔行列式的锐界

摘要本文证明了星形函数𝑓的尖锐不等式| h3,1 (f) |≤4/9 \lvert H＿3,1{(f) }\rvert\leq /9，其中h3,1 (f) {H＿3,1}(f)是第三汉克尔行列式，从而解决了一个长期存在的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.