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Keywords = succesive coefficients

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15 pages, 309 KiB  
Article
Coefficient Inequalities for Biholomorphic Mappings on the Unit Ball of a Complex Banach Space
by Hidetaka Hamada, Gabriela Kohr and Mirela Kohr
Mathematics 2022, 10(24), 4832; https://doi.org/10.3390/math10244832 - 19 Dec 2022
Cited by 1 | Viewed by 1602
Abstract
In the first part of this paper, we give generalizations of the Fekete–Szegö inequalities for quasiconvex mappings F of type B and the first elements F of g-Loewner chains on the unit ball of a complex Banach space, recently obtained by H. [...] Read more.
In the first part of this paper, we give generalizations of the Fekete–Szegö inequalities for quasiconvex mappings F of type B and the first elements F of g-Loewner chains on the unit ball of a complex Banach space, recently obtained by H. Hamada, G. Kohr and M. Kohr. We obtain the Fekete–Szegö inequalities using the norm under the restrictions on the second and third order terms of the homogeneous polynomial expansions of the mappings F. In the second part of this paper, we give the estimation of the difference of the moduli of successive coefficients for the first elements of g-Loewner chains on the unit disc. We also give the estimation of the difference of the moduli of successive coefficients for the first elements F of g-Loewner chains on the unit ball of a complex Banach space under the restrictions on the second and third order terms of the homogeneous polynomial expansions of the mappings F. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
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