An application of fractional calculus to a new class of multivalent functions with negative coefficients

Motivated by some earlier works of Chen et al. (cf., [1,2]), dealing with various ap plications of the operators of fractional calculus in Analytic Function Theory, the authors introduce and study rather systematically a certain subclass of analytic and p-valent functions with negative coefficients. This subclass is defined by using a familiar fractional derivative operator. Coefficient estimates, growth and distortion theorems, and many other interesting and useful properties and characteristics of this class of analytic and p-valent functions are obtained; some of these properties involve, for example, linear combinations and modified Hadamard products (or convolution) of functions belonging to the class introduced here. (C) 1999 Elsevier Science Ltd. All rights reserved.