Subclasses of meromorphically multivalent functions defined by a differential operator

Details Subclasses of meromorphically multivalent functions defined by a differential operator Subclasses of meromorphically multivalent functions defined by a differential operator

2010-08-27

arxiv.org/abs/1008.4691v1

Comput. Math. Appl. 61 (2011) 966-979

Mathematics

Complex Variables

Scientific paper

In this paper we introduce and study two new subclasses \Sigma_{\lambda\mu mp}(\alpha,\beta)$ and $\Sigma^{+}_{\lambda\mu mp}(\alpha,\beta)$ of meromorphically multivalent functions which are defined by means of a new differential operator. Some results connected to subordination properties, coefficient estimates, convolution properties, integral representation, distortion theorems are obtained. We also extend the familiar concept of $% (n,\delta)-$neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions.

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