一类星状函数的h3(1)猜想

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca 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

摘要

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 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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来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.