Geodesic
Sharp bounds associated with the Zalcman conjecture for the initial coefficients and second Hankel determinants for certain subclass of analytic functions
Matematičeskie zametki SVFU, Tome 30 (2023) no. 2, pp. 92-100

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In this paper, we obtain sharp bounds in the Zalcman conjecture for the initial coe cients, the second Hankel determinant $H_{2,2}(f) = a_2a_4 - a^2_3$ and an upper bound for the second Hankel determinant $H_{2,3}(f) = a_3a_5-a_2$ for the functions belonging to a certain subclass of analytic functions. The practical tools applied in the derivation of our main results are the coe cient inequalities of the Caratheodory class $P$.
Keywords: analytic function, upper bound, the Zalcman conjecture, univalent function, Caratheodory function. 
N. Vani; D. Vamshee Krishna; B. Rath. Sharp bounds associated with the Zalcman conjecture for the initial coefficients and second Hankel determinants for certain subclass of analytic functions. Matematičeskie zametki SVFU, Tome 30 (2023) no. 2, pp. 92-100. http://geodesic.mathdoc.fr/item/SVFU_2023_30_2_a6/
@article{SVFU_2023_30_2_a6,
     author = {N. Vani and D. Vamshee Krishna and B. Rath},
     title = {Sharp bounds associated with the {Zalcman} conjecture for the initial coefficients and second {Hankel} determinants for certain subclass of analytic functions},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {92--100},
     year = {2023},
     volume = {30},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2023_30_2_a6/}
}
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