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Zbl 1165.30005
Neighborhoods of a certain class of analytic functions with negative coefficients.
(English)
[J] Banach J. Math. Anal. 3, No. 1, 111-121, electronic only (2009). ISSN 1735-8787/e

The author introduces a subclass of analytic functions in the open disc with negative coefficients. This new class is defined by means of multiplier transformations. Using the familiar concept of neighborhoods of analytic functions, the author proves coefficient inequalities, distortion theorems and associated inclusion relations for the $(n,\delta)$-neighborhoods of functions belonging to the new class, which satisfy a certain nonhomogeneous Cauchy-Euler differential equation.
[Arun Kumar Agarwal (Ruston)]
MSC 2000:
*30C45 Special classes of univalent and multivalent functions
30C50 Coefficient problems for univalent and multivalent functions

Keywords: analytic function with negative coefficients; $(n,\delta)$-neighborhood of an analytic function

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