Sharp bounds associated with the Zalcman conjecture for the initial coefficients and second Hankel determinants for certain subclass of analytic functions
https://doi.org/10.25587/SVFU.2023.24.67.007
Аннотация
In this paper, we obtain sharp bounds in the Zalcman conjecture for the initial coefficients, the second Hankel determinant H2,2(f) = a2a4 − a24 and an upper bound for the second Hankel determinant H2,3(f) = a3a5−a24 for the functions belonging to a certain subclass of analytic functions. The practical tools applied in the derivation of our main results are the coefficient inequalities of the Carath´eodory class P.
Ключевые слова
Об авторах
N. Vani
Department of Mathematics, GITAM School of Science,
GITAM University
Индия
Индия
D. Vamshee Krishna
Department of Mathematics, GITAM School of Science,
GITAM University
Индия
Индия
B. Rath
Россия
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Рецензия
Для цитирования:
Vani N., Vamshee Krishna D., Rath B. Sharp bounds associated with the Zalcman conjecture for the initial coefficients and second Hankel determinants for certain subclass of analytic functions. Математические заметки СВФУ. 2023;30(2):92-100. https://doi.org/10.25587/SVFU.2023.24.67.007
For citation:
Vani N., Vamshee Krishna D., Rath B. Sharp bounds associated with the Zalcman conjecture for the initial coefficients and second Hankel determinants for certain subclass of analytic functions. Mathematical notes of NEFU. 2023;30(2):92-100. https://doi.org/10.25587/SVFU.2023.24.67.007
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