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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 $${\cal U}_k[p, \alpha, \beta, A,B],$$ $$(p, k\in\bbfN:= \{1,2,3,\dots,\};\quad 0\le\alpha< p;\quad \beta\ge 0;\quad -1\le A< B\le 1;\quad 0< B\le 1),$$ 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 ${\cal U}_k[p, \alpha,\beta, A,B]$.

30C45Special classes of univalent and multivalent functions
Full Text: DOI
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