Fekete-Szegö problem for a new class of analytic functions defined by using a generalized differential operator. (English) Zbl 1291.30059

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

Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 52, No. 1, 21-34 (2013).

Summary: In this paper, we obtain Fekete-Szegö inequalities for a generalized class of analytic functions \(f(z)\in \mathcal {A} \) for which \(1+\frac{1}{b}\bigg(\frac{z(D_{\alpha ,\beta ,\lambda ,\delta}^{n} f(z))'}{D_{\alpha ,\beta ,\lambda ,\delta}^{n}f(z)}-1\bigg)\) (\(\alpha ,\beta ,\lambda ,\delta \geq 0\); \(\beta >\alpha\); \(\lambda >\delta\); \(b \in \mathbb {C}^{\ast}\); \(n \in \mathbb {N}_{0}\); \(z \in U\)) lies in a region starlike with respect to \(1\) and is symmetric with respect to the real axis.

MSC:

30C45

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

analytic; subordination; Fekete-Szegö problem

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