matmessМатематические заметки СВФУMathematical notes of NEFU2411-93262587-876XСеверо-Восточный федеральный университет имени М.К. Аммосова10.25587/SVFU.2023.24.67.007matmess-109Research ArticleМАТЕМАТИКАSharp bounds associated with the Zalcman conjecture for the initial coefficients and second Hankel determinants for certain subclass of analytic functionsSharp bounds associated with the Zalcman conjecture for the initial coefficients and second Hankel determinants for certain subclass of analytic functionsVaniN.VaniN.

Visakhapatnam-530 045, A. P., India

vnallmot@gitam.inVamshee KrishnaD.Vamshee KrishnaD.

Visakhapatnam-530 045, A. P., India

vamsheekrishna1972@gmail.comRathB.RathB.

Visakhapatnam-530 045, A. P., India

brath@gitam.eduDepartment of Mathematics, GITAM School of Science, GITAM UniversityIndia20233006202330292100Copyright © Vani N., Vamshee Krishna D., Rath B., 20232023Vani N., Vamshee Krishna D., Rath B.Vani N., Vamshee Krishna D., Rath B.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://matmess.elpub.ru/jour/article/view/109

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.

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.

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The authors declare that there are no conflicts of interest present.