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The Sharp Bounds of the Second and Third Hankel Determinants for the Class $\mathcal{SL}*$

In: Mathematica Slovaca, vol. 70, no. 4
Shagun Banga - S. Sivaprasad Kumar
Detaily:
Rok, strany: 2020, 849 - 862
Kľúčové slová:
Hankel determinant, Lemniscate of Bernoulli, Carath´eodory coefficients, Zalcman functional
O článku:
In this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Carathéodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants $H3(1)$ and $H2(3)$ for the well known class $\mathcal{SL}*$ of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional: $|a32-a5|$ for the class $\mathcal{SL}*$ is also estimated. Further, a couple of interesting results of $\mathcal{SL}*$ are also discussed.
Ako citovať:
ISO 690:
Banga, S., Kumar, S. 2020. The Sharp Bounds of the Second and Third Hankel Determinants for the Class $\mathcal{SL}*$. In Mathematica Slovaca, vol. 70, no.4, pp. 849-862. 0139-9918.

APA:
Banga, S., Kumar, S. (2020). The Sharp Bounds of the Second and Third Hankel Determinants for the Class $\mathcal{SL}*$. Mathematica Slovaca, 70(4), 849-862. 0139-9918.
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 24. 7. 2020