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Some properties associated to a certain class of starlike functions

In: Mathematica Slovaca, vol. 69, no. 6
Vali Soltani Masih - Ali Ebadian - Sibel Yalçin

Details:

Year, pages: 2019, 1329 - 1340
Keywords:
univalent functions; subordination; logarithmic coefficients; starlike functions; domain bounded by cissoid of Diocles
About article:
Let $\mathcal{A}$ denote the family of analytic functions $f$ with $f(0)=f'(0)-1=0$, in the open unit disk $Δ$. We consider a class \[ \mathcal{S}*cs(α):=\{f\in\mathcal{A} : (((zf'(z)) / (f(z)))-1)\prec ((z) / (1+(α-1) z-α z2)), z\in Δ\}, \] where $0≤α≤ 1/2$, and $\prec$ 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 $f\in \mathcal{S}*cs(α)$: \[ ∑n=1n|2 ≤ ((1) / (4(1+α)2))(((π2) / (6))-2 \mathrm{Li}2(-α)+ \mathrm{Li}22)), \] where $\mathrm{Li\mspace{1mu}2}$ denotes the dilogarithm function are investigated.
How to cite:
ISO 690:
Masih, V., Ebadian, A., Yalçin, S. 2019. Some properties associated to a certain class of starlike functions. In Mathematica Slovaca, vol. 69, no.6, pp. 1329-1340. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0311

APA:
Masih, V., Ebadian, A., Yalçin, S. (2019). Some properties associated to a certain class of starlike functions. Mathematica Slovaca, 69(6), 1329-1340. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0311
About edition:
Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Published: 22. 12. 2019