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On neighborhoods of analytic functions defined by using Hadamard product. (English) Zbl 1164.30010

Let \(A(n)\) denote the class of functions \(f\) of the form \(f(z)=z-\sum_{k=n+1}^\infty a_kz^k\) (\(a_k\geq0\), \(k=2,3,\dots\), \(n=1,2,\dots\)) which are analytic in the unit disc \(| z| <1\). By using the Hadamard product \(f*S_\alpha(z)=\dfrac{z}{(1-z)^{2(1-\alpha)}}\), the classes \(S_n(\gamma,\beta,\alpha)\) and \(R_n(\gamma,\beta,\alpha;\mu)\) are introduced. The author considers the \((n,\delta)\)-neighborhoods of these classes of analytic functions.

MSC:

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