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

Abstract

Motivated by some earlier works of Chen et al. (cf., [1,2]), dealing with various applications 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.