Back to Search
Start Over
Some properties associated to a certain class of starlike functions.
- Source :
-
Mathematica Slovaca . Dec2019, Vol. 69 Issue 6, p1329-1340. 12p. - Publication Year :
- 2019
-
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]
Details
- Language :
- English
- ISSN :
- 01399918
- Volume :
- 69
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Mathematica Slovaca
- Publication Type :
- Academic Journal
- Accession number :
- 140960091
- Full Text :
- https://doi.org/10.1515/ms-2017-0311