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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 — 2013

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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

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