Second Hankel determinant for a class of analytic functions defined by a linear operator

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Published: Sep 30, 2012
DOI: https://doi.org/10.5556/j.tkjm.43.2012.518
Keywords:
Fekete-Szegö functional Hankel determinant Positive real functions Linear operator.

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Aabed Mohammed
School ofMathematical Sceinces, Faculty of Science and Technology,Universiti KebangsaanMalaysia 43600 Bangi, Selangor D. Ehsan,Malaysia.
Maslina Darus
School ofMathematical Sceinces, Faculty of Science and Technology,Universiti KebangsaanMalaysia 43600 Bangi, Selangor D. Ehsan,Malaysia.

Abstract

By making use of the linear operator $\Theta _m^{\lambda ,n} ,\,\,m \in \mathbb{N}=\{1,2,3,\ldots\}$ and $\lambda \,,\,n \in \mathbb{N}_0 = \mathbb{N} \cup \{ 0\}$ given by the authors, a class of analytic functions $S_m^{\lambda ,n}(\alpha ,\sigma ) ( {| \alpha| < \pi/2}, \; 0\leq \sigma <1) $ is introduced. The object of the present paper is to obtain sharp upper bound for functional $ \left| {\,a_2 a_4 - a_3 ^2 } \right|.$

Article Details

How to Cite
Mohammed, A., & Darus, M. (2012). Second Hankel determinant for a class of analytic functions defined by a linear operator. Tamkang Journal of Mathematics, 43(3), 455–462. https://doi.org/10.5556/j.tkjm.43.2012.518
Issue
Vol. 43 No. 3 (2012)
Section
Papers
Author Biographies

Aabed Mohammed, School ofMathematical Sceinces, Faculty of Science and Technology,Universiti KebangsaanMalaysia 43600 Bangi, Selangor D. Ehsan,Malaysia.

School ofMathematical Sceinces, Faculty of Science and Technology,Universiti KebangsaanMalaysia 43600 Bangi,Selangor D. Ehsan,Malaysia.

Maslina Darus, School ofMathematical Sceinces, Faculty of Science and Technology,Universiti KebangsaanMalaysia 43600 Bangi, Selangor D. Ehsan,Malaysia.

School ofMathematical Sceinces, Faculty of Science and Technology,Universiti KebangsaanMalaysia 43600 Bangi, Selangor D. Ehsan,Malaysia.

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