Second Hankel determinat for certain analytic functions satisfying subordinate condition

Rok, strany: 2018, 463 - 471

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.

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