Abstract

In this paper, we introduce a new subclass $S^{p,q,s}_{\alpha,\beta,j}(\gamma)$ of certain analytic functions defined by a differential operator. A majorization problem for functions belonging to class $S^{p,q,s}_{\alpha,\beta,j}(\gamma)$ is considered. Moreover we point out some consequences of our main result. As well as using principal of subordination, we obtain inclusion properties of certain subclasses of analytic functions defined using that differential operator and inclusion properties of these classes involving the generalized integral operator.

Keywords and Phrases

Analytic functions, multivalent functions, differential subordinations, Hadamard product, differential operator, integral operator.

A.M.S. subject classification

30C45.

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