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

Authors

  • 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.

DOI:

https://doi.org/10.5556/j.tkjm.43.2012.518

Keywords:

Fekete-Szegö functional, Hankel determinant, Positive real functions, Linear operator.

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|.$

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.

References

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Published

2012-09-30

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

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