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Neighborhoods for certain analytic functions. (English) Zbl 1354.30011

Summary: In this paper, we introduce the neighborhood \(\mathcal{N}_{\delta}(\alpha,\beta,\lambda;g)\) of analytic functions \(f\) and \(g\) defined in the open unit disc. Furthermore, we derive some sufficient and necessary conditions to be in \(\mathcal{N}_{\delta}(\alpha,\beta,\lambda;g)\). In addition, we see some applications of Jack’s lemma.

MSC:

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

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