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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)
  • Received : 2014.08.14
  • Published : 2015.11.01

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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