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

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.


30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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