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Second Hankel determinat for certain analytic functions satisfying subordinate condition

In: Mathematica Slovaca, vol. 68, no. 2
Erhan Deniz - Levent Budak

Details:

Year, pages: 2018, 463 - 471
Keywords:
analytic functions, starlike functions, convex functions, Ma-Minda starlike functions, Ma-Minda convex functions, subordination, second Hankel determinant
About article:
In this paper, we introduce and investigate the following subclass%

$$ 1+((1) / (γ))(((zf'(z)+λ z2f''(z)) / (λ zf'(z)+(1-λ)f(z)))-1) \prec φ (z)  (0≤ λ ≤ 1,γ \in \mathbb{C}\smallsetminus \{0\}) $$

of analytic functions, $φ$ is an analytic function with positive real part in the unit disk $\mathbb{D}$, satisfying $φ (0)=1$, $φ'(0)>0$, and $φ (\mathbb{D})$ is symmetric with respect to the real axis. We obtain the upper bound of the second Hankel determinant $\vert a2a4-a32\vert$ for functions belonging to the this class is studied using Toeplitz determinants. The results, which are presented in this paper, would generalize those in related works of several earlier authors.
How to cite:
ISO 690:
Deniz, E., Budak, L. 2018. Second Hankel determinat for certain analytic functions satisfying subordinate condition. In Mathematica Slovaca, vol. 68, no.2, pp. 463-471. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0116

APA:
Deniz, E., Budak, L. (2018). Second Hankel determinat for certain analytic functions satisfying subordinate condition. Mathematica Slovaca, 68(2), 463-471. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0116
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