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Applications of extremal theorem and radius equation for a class of analytic functions

In: Mathematica Slovaca, vol. 66, no. 6
Liangpeng Xiong - Xiaoli Liu
Detaily:
Rok, strany: 2016, 1319 - 1328
Kľúčové slová:
analytic functions, linear topologial structure, Hadamard product, radius equation, extreme points, distortion inequality
O článku:
A linear operator $D_{\mathcal{P}k}f(z): S\rightarrow S$ is introduced, where $S$ denotes the class of univalent analytic functions in open unit disk and $\mathcal{P}k$ is an arbitrary monotonically increasing function in $k$. We study a new class $\mathscr{T}_{\mathcal{P}k}(α123,β)$ of analytic functions related to $D_{\mathcal{P}k}f(z)$. The main object of this paper is to give the radius equation between the class $\mathscr{T}_{\mathcal{P}k}(α123,β)$ and the close-to-convex class of order $α$ $(0≤α<1)$. Also, we apply the extremal theorem to maximize $|f^{(\mathcal{X})}(z)|$ over $\mathscr{T}_{\mathcal{P}k}(α123,β)$, where $\mathcal{X}=\{0,1,2,…,k\}$, all the results are sharp.
Ako citovať:
ISO 690:
Xiong, L., Liu, X. 2016. Applications of extremal theorem and radius equation for a class of analytic functions. In Mathematica Slovaca, vol. 66, no.6, pp. 1319-1328. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0225

APA:
Xiong, L., Liu, X. (2016). Applications of extremal theorem and radius equation for a class of analytic functions. Mathematica Slovaca, 66(6), 1319-1328. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0225
O vydaní:
Publikované: 1. 12. 2016