1. Some properties associated to a certain class of starlike functions.
- Author
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Masih, Vali Soltani, Ebadian, Ali, and Yalçin, Sibel
- Subjects
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STAR-like functions , *GEOMETRIC function theory , *ANALYTIC functions , *GEOMETRIC approach , *UNIVALENT functions , *CHARACTERISTIC functions - Abstract
Let 𝓐 denote the family of analytic functions f with f(0) = f′(0) – 1 = 0, in the open unit disk Δ. We consider a class S c s ∗ (α) := f ∈ A : z f ′ (z) f (z) − 1 ≺ z 1 + α − 1 z − α z 2 , z ∈ Δ , $$\begin{array}{} \displaystyle \mathcal{S}^{\ast}_{cs}(\alpha):=\left\{f\in\mathcal{A} : \left(\frac{zf'(z)}{f(z)}-1\right)\prec \frac{z}{1+\left(\alpha-1\right) z-\alpha z^2}, \,\, z\in \Delta\right\}, \end{array}$$ 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 coefficients γn of f ∈ S c s ∗ $\begin{array}{} \mathcal{S}^{\ast}_{cs} \end{array}$ (α): ∑ n = 1 ∞ γ n 2 ≤ 1 4 1 + α 2 π 2 6 − 2 L i 2 − α + L i 2 α 2 , $$\begin{array}{} \displaystyle \sum_{n=1}^{\infty}\left|\gamma_n\right|^2 \leq \frac{1}{4\left(1+\alpha\right)^2}\left(\frac{\pi^2}{6}-2 \mathrm{Li}_2\left(-\alpha\right)+ \mathrm{Li}_2\left(\alpha^2\right)\right), \end{array}$$ where Li2 denotes the dilogarithm function are investigated. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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