Some properties associated to a certain class of starlike functions
| Autor: | Sibel Yalçın, Ali Ebadian, Vali Soltani Masih |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Mathematica Slovaca. 69:1329-1340 |
| ISSN: | 1337-2211 0139-9918 |
| DOI: | 10.1515/ms-2017-0311 |
| Popis: | Let 𝓐 denote the family of analytic functionsfwithf(0) =f′(0) – 1 = 0, in the open unit disk Δ. We consider a class$$\begin{array}{} \displaystyle \mathcal{S}^{\ast}_{cs}(\alpha):=\left\{f\in\mathcal{A} : \left(\frac{zf'(z)}{f(z)}-1\right)\prec \frac{z}{1+\left(\alpha-1\right) z-\alpha z^2}, \,\, z\in \Delta\right\}, \end{array}$$where 0 ≤α≤ 1/2, and ≺ is the subordination relation. The methods and techniques of geometric function theory are used to get characteristics of the functions in this class. Further, the sharp inequality for the logarithmic coefficientsγnoff∈$\begin{array}{} \mathcal{S}^{\ast}_{cs} \end{array}$(α):$$\begin{array}{} \displaystyle \sum_{n=1}^{\infty}\left|\gamma_n\right|^2 \leq \frac{1}{4\left(1+\alpha\right)^2}\left(\frac{\pi^2}{6}-2 \mathrm{Li}_2\left(-\alpha\right)+ \mathrm{Li}_2\left(\alpha^2\right)\right), \end{array}$$where Li2denotes the dilogarithm function are investigated. |
| Databáze: | OpenAIRE |
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