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.


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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