Fekete–Szegö Problem for a New Class of Analytic Functions Defined by Using a Generalized Differential Operator

M. K. Aouf; R. M. El-Ashwah; A. A. M. Hassan; A. H. Hassan

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2013)

  • Volume: 52, Issue: 1, page 21-34
  • ISSN: 0231-9721

Abstract

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In this paper, we obtain Fekete–Szegö inequalities for a generalized class of analytic functions f ( z ) ∈ 𝒜 for which 1 + 1 b z D α , β , λ , δ n f ( z ) ' D α , β , λ , δ n f ( z ) - 1 ( α , β , λ , δ ≥ 0 ; β > α ; λ > δ ; b ∈ ℂ * ; n ∈ ℕ 0 ; z ∈ U ) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis.

How to cite

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Aouf, M. K., et al. "Fekete–Szegö Problem for a New Class of Analytic Functions Defined by Using a Generalized Differential Operator." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 52.1 (2013): 21-34. <http://eudml.org/doc/260599>.

@article{Aouf2013,
abstract = {In this paper, we obtain Fekete–Szegö inequalities for a generalized class of analytic functions $f(z)\in \mathcal \{A\} $ for which $1+\frac\{1\}\{b\}\Big ( \frac\{z\left( D_\{\alpha ,\beta ,\lambda ,\delta \}^n f(z)\right)^\{\prime \}\}\{D_\{\alpha ,\beta ,\lambda ,\delta \}^\{n\}f(z)\}-1\Big )$ ($\alpha ,\beta ,\lambda ,\delta \ge 0$; $\beta >\alpha $; $\lambda >\delta $; $b\in \mathbb \{C\}^\{\ast \}$; $n\in \mathbb \{N\}_\{0\}$; $z\in U$) lies in a region starlike with respect to $1$ and is symmetric with respect to the real axis.},
author = {Aouf, M. K., El-Ashwah, R. M., Hassan, A. A. M., Hassan, A. H.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {analytic; subordination; Fekete–Szegö problem; analytic; subordination; Fekete-Szegö problem},
language = {eng},
number = {1},
pages = {21-34},
publisher = {Palacký University Olomouc},
title = {Fekete–Szegö Problem for a New Class of Analytic Functions Defined by Using a Generalized Differential Operator},
url = {http://eudml.org/doc/260599},
volume = {52},
year = {2013},
}

TY - JOUR
AU - Aouf, M. K.
AU - El-Ashwah, R. M.
AU - Hassan, A. A. M.
AU - Hassan, A. H.
TI - Fekete–Szegö Problem for a New Class of Analytic Functions Defined by Using a Generalized Differential Operator
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2013
PB - Palacký University Olomouc
VL - 52
IS - 1
SP - 21
EP - 34
AB - In this paper, we obtain Fekete–Szegö inequalities for a generalized class of analytic functions $f(z)\in \mathcal {A} $ for which $1+\frac{1}{b}\Big ( \frac{z\left( D_{\alpha ,\beta ,\lambda ,\delta }^n f(z)\right)^{\prime }}{D_{\alpha ,\beta ,\lambda ,\delta }^{n}f(z)}-1\Big )$ ($\alpha ,\beta ,\lambda ,\delta \ge 0$; $\beta >\alpha $; $\lambda >\delta $; $b\in \mathbb {C}^{\ast }$; $n\in \mathbb {N}_{0}$; $z\in U$) lies in a region starlike with respect to $1$ and is symmetric with respect to the real axis.
LA - eng
KW - analytic; subordination; Fekete–Szegö problem; analytic; subordination; Fekete-Szegö problem
UR - http://eudml.org/doc/260599
ER -

References

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