Geodesic
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, Tome 52 (2013) no. 1, pp. 21-34 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 30C45
Keywords: analytic; subordination; Fekete–Szegö problem 
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     title = {Fekete{\textendash}Szeg\"o {Problem} for a {New} {Class} of {Analytic} {Functions} {Defined} by {Using} a {Generalized} {Differential} {Operator}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
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Aouf, M. K.; El-Ashwah, R. M.; Hassan, A. A. M.; Hassan, A. H. 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, Tome 52 (2013) no. 1, pp. 21-34. http://geodesic.mathdoc.fr/item/AUPO_2013_52_1_a1/