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A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients. (English) Zbl 0760.30006

Making use of a certain operator of fractional derivatives, a new subclass \({\mathcal J}_ p(\alpha,\beta,\lambda)\) of analytic and \(p\)-valent functions with negative coefficients is introduced and studied here rather systematically. Coefficient estimates, distortion theorems, and various other interesting and useful properties of this class of functions are given; some of these properties involve, for example, linear combinations and modified Hadamard products of several functions belonging to the class introduced here.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
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