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http://dx.doi.org/10.4134/JKMS.2015.52.6.1139

THIRD ORDER HANKEL DETERMINANT FOR CERTAIN UNIVALENT FUNCTIONS  

BANSAL, DEEPAK (DEPARTMENT OF MATHEMATICS GOVT. COLLEGE OF ENGINEERING AND TECHNOLOGY)
MAHARANA, SUDHANANDA (DEPARTMENT OF MATHEMATICS CENTRAL UNIVERSITY OF RAJASTHAN)
PRAJAPAT, JUGAL KISHORE (DEPARTMENT OF MATHEMATICS CENTRAL UNIVERSITY OF RAJASTHAN)
Publication Information
Journal of the Korean Mathematical Society / v.52, no.6, 2015 , pp. 1139-1148 More about this Journal
Abstract
The estimate of third Hankel determinant $$H_{3,1}(f)=\left|a_1\;a_2\;a_3\\a_2\;a_3\;a_4\\a_3\;a_4\;a_5\right|$$ of the analytic function $f(z)=z+a2z^2+a3z^3+{\cdots}$, for which ${\Re}(1+zf^{{\prime}{\prime}}(z)/f^{\prime}(z))>-1/2$ are investigated. The corrected version of a known results [2, Theorem 3.1 and Theorem 3.3] are also obtained.
Keywords
analytic functions; univalent function; close-to-convex functions; starlike functions; Fekete-$Szeg{\ddot{o}}$ functional; Hankel determinant;
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