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A unified presentation of some classes of meromorphically multivalent functions. (English) Zbl 0978.30011

Summary: The authors introduce and investigate various properties of a general class \[ {\mathcal U}_k[p, \alpha, \beta, A,B], \]
\[ (p, k\in\mathbb{N}:= \{1,2,3,\dots,\};\quad 0\leq\alpha< p;\quad \beta\geq 0;\quad -1\leq A< B\leq 1;\quad 0< B\leq 1), \] which unifies and extends several (known or new) subclasses of meromorphically multivalent functions. The properties and characteristics of this general class, which are presented here, include growth and distortion theorems; they also involve Hadamard products (or convolution) of functions belonging to the class \({\mathcal U}_k[p, \alpha,\beta, A,B]\).

MSC:

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