Unified solution of Fekete-Szegö problem for subclasses of starlike mappings in several complex variables

Rok, strany: 2019, 843 - 856

Let $\mathcal {S}^*_ψ$ be a subclass of starlike functions in the unit disk $\mathbb{U},$ where $ψ$ is a convex function such that $ψ(0)=1$, $ψ'(0)>0$, $\Re\big(ψ(ξ)\big)>0$ and $ψ(\mathbb{U})$ is symmetric with respect to the real axis. We obtain the sharp solution of Fekete-Szegö problem for the family $\mathcal {S}^*_ψ$, and then extend the result to the case of corresponding subclass defined on the bounded starlike circular domain $Ω$ in several complex variables, which give an unified answer of Fekete-Szegö problem for the kinds of subclasses of starlike mappings defined on $Ω$. At last, we propose two conjectures related the same problems on the unit ball in a complex Banach space and on the unit polydisk in $\mathbb{C}ⁿ$.

ISO 690:

Tu, Z., Xiong, L. 2019. Unified solution of Fekete-Szegö problem for subclasses of starlike mappings in several complex variables. In Mathematica Slovaca, vol. 69, no.4, pp. 843-856. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0273

APA:

Tu, Z., Xiong, L. (2019). Unified solution of Fekete-Szegö problem for subclasses of starlike mappings in several complex variables. Mathematica Slovaca, 69(4), 843-856. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0273

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava