Some results of homogeneous expansions for a class of biholomorphic mappings defined on a Reinhardt domain in ℂn

• Autorzy: Sima Xiaoying , Tu Zhenhan , Xiong Liangpeng

Identyfikatory

DOI

10.1515/dema-2022-0242

• Języki publikacji: EN

Abstrakty

EN

Let S*γ,A,B(D) be the usual class of g -starlike functions of complex order γ in the unit disk D={ζ∈C:∣ζ∣<1} , where g(ζ)=(1+Aζ)∕(1+Bζ) , with γ∈C\{0},−1 ≤A < B ≤1,ζ∈D. First, we obtain the bounds of all the coefficients of homogeneous expansions for the functions f∈S*γ,A,B(D) when ζ=0 is a zero of order k+1 of f(ζ)−ζ . Second, we generalize this result to several complex variables by considering the corresponding biholomorphic mappings defined in a bounded complete Reinhardt domain. These main theorems unify and extend many known results.

Słowa kluczowe

EN

biholomorphic mappings; coefficient problems; Reinhardt domain; g-starlike mappings of complex order gamma

PL

odwzorowania holomorficzne; współczynnik; odwzorowania gwiaździste

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220242
• Opis fizyczny: Bibliogr. 36 poz.

Twórcy

autor

Sima Xiaoying

• School of Mathematics and Computer Science, Jiangxi Science and Technology Normal University, Nanchang 330038, Jiangxi, People’s Republic of China

autor

Tu Zhenhan

• School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, People’s Republic of China

autor

Xiong Liangpeng

• School of Mathematics and Computer Science, Jiangxi Science and Technology Normal University, Nanchang 330038, Jiangxi, People’s Republic of China

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).