Abstract
AbstractThe paper is devoted to the study of a family of complex-valued holomorphic functions and a family of holomorphic mappings in $${\mathbb {C}}^{n}.$$
C
n
.
More precisely, the article concerns a Bavrin’s family of functions defined on a bounded complete n-circular domain $${\mathcal {G}}$$
G
of $${\mathbb {C}}^{n}$$
C
n
and a family of biholomorphic mappings on the Euclidean open unit ball in $${\mathbb {C}}^{n}.$$
C
n
.
The presented results include some estimates of a combination of the Fréchet differentials at the point $$z=0,$$
z
=
0
,
of the first and second order for Bavrin’s functions, also of the second and third order for biholomorphic close-to-starlike mappings in $${\mathbb {C}}^{n},$$
C
n
,
respectively. These bounds give a generalization of the Fekete–Szegö coefficients problem for holomorphic functions of a complex variable on the case of holomorphic functions and mappings of several variables.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Algebra and Number Theory,Analysis
Reference34 articles.
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3. Długosz, R., Leś, E.: Embedding theorems and extremal problems for holomorphic functions on circular domains of $${\mathbb{C} }^{n}$$. Complex Var. Elliptic Equ. 59, 883–899 (2014)
4. Długosz, R., Liczberski, P.: Some results of Fekete–Szegö type for Bavrin’s families of holomorphic functions in $${\mathbb{C}}^{n}$$. Ann. Mat. Pura Appl. (1923-), 200, 1841-1857 (2021)
5. Długosz, R., Liczberski, P.: Some results of Fekete–Szegö type. Results for some holomorphic functions of several complex variables. Symmetry 12, Art. nr. 1707, 1-10 (2020)
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