A Conjecture on H ₃(1) for Certain Starlike Functions

Pub Date : 2023-10-01 DOI:10.1515/ms-2023-0088

Neha Verma, S. Sivaprasad Kumar

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引用次数: 3

Abstract

ABSTRACT We prove a conjecture concerning the third Hankel determinant, proposed by Kumar and Kamaljeet in [A cardioid domain and starlike functions , Anal. Math. Phys. 11 (2021), Art. 54], which states that | H 3 (1)| ≤ 1/9 is sharp for the class S ℘ * = { z f ′ ( z ) / f ( z ) ≺ φ ( z ) : = 1 + z e z } . In addition, we also establish bounds for sixth and seventh coefficient, and | H 4 (1)| for functions in S ℘ * . The general bounds for two and three folds symmteric functions related with the Ma-Minda classes S * ( φ ) of starlike functions are also obtained.

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一类星状函数的h3(1)猜想

摘要证明了由Kumar和Kamaljeet在[a]心域和星形函数中提出的关于第三Hankel行列式的一个猜想。数学。Phys. 11 (2021)， Art. 54]，其中指出| h3(1)|≤1/9对于S - p类是尖锐的* = {z f ' (z) / f (z) φ (z): = 1 + z e z}。此外，我们还建立了S - p *中函数的第六和第七系数的界，以及S - p *中的函数的界| h4(1)|。得到了与星形函数的Ma-Minda类S * (φ)相关的二叠和三叠对称函数的一般界。

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A Conjecture on H 3(1) for Certain Starlike Functions

Abstract

A Conjecture on H ₃(1) for Certain Starlike Functions