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Second hankel determinat for certain analytic functions satisfying subordinate condition

  • Erhan Deniz EMAIL logo and Levent Budak
Published/Copyright: March 31, 2018
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Abstract

In this paper, we introduce and investigate the following subclass

1+1γzf(z)+λz2f(z)λzf(z)+(1λ)f(z)1φ(z)0λ1,γC{0}

of analytic functions, φ is an analytic function with positive real part in the unit disk 𝔻, satisfying φ (0) = 1, φ '(0) > 0, and φ (𝔻) is symmetric with respect to the real axis. We obtain the upper bound of the second Hankel determinant | a2a4a32 | 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.


Communicated by Stanis lava Kanas


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Received: 2015-11-20
Accepted: 2016-5-15
Published Online: 2018-3-31
Published in Print: 2018-4-25

© 2018 Mathematical Institute Slovak Academy of Sciences

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