Sufficient conditions for Carathéodory functions and applications to univalent functions

Rok, strany: 2019, 1065 - 1076

In this paper, the authors derive several sufficient conditions for a function to be the Carathéodory function in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}: |z|<1 \}$. More precisely, for given $β \in (-π/2,π/2)$, $γ \in [0,\cosβ)$ and $δ\in(0,π/2]$, we find some sufficient conditions for an analytic function $p$ such that $p(0)=1$ to satisfy ${\re}\{{\e}^{-{\ii}β} p(z) \} > γ$ or $| \arg \{p(z)-γ\} |<δ$ for all $z\in\mathbb{D}$ by using the first-order differential subordination. We then apply the results obtained here in order to find some conditions for univalent functions with geometric properties such as spirallikeness and strongly starlikeness.

ISO 690:

Kwon, O., Sim, Y. 2019. Sufficient conditions for Carathéodory functions and applications to univalent functions. In Mathematica Slovaca, vol. 69, no.5, pp. 1065-1076. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0290

APA:

Kwon, O., Sim, Y. (2019). Sufficient conditions for Carathéodory functions and applications to univalent functions. Mathematica Slovaca, 69(5), 1065-1076. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0290

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava