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A Conjecture on H3(1) for Certain Starlike Functions

  • Neha Verma and S. Sivaprasad Kumar EMAIL logo
From the journal Mathematica Slovaca

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 |H3(1)| ≤ 1/9 is sharp for the class S*={zf(z)/f(z)φ(z):=1+zez} . In addition, we also establish bounds for sixth and seventh coefficient, and |H4(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.

2020 Mathematics Subject Classification: Primary 30C45; Secondary 30C50

(Communicated by Stanisława Kanas)


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Received: 2022-08-05
Accepted: 2022-12-12
Published Online: 2023-10-07

© 2023 Mathematical Institute Slovak Academy of Sciences

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