A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients
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.
scientific article; zbMATH DE number 150675