On a new class of p-valent functions with negative coefficients

Abstract

In this paper, we introduce the class A ∗ (p, A, B, α) of p-valent functions in the unit disc U = {z ∈ C : |z| < 1} . We give basic properties of functions belonging to this class and obtain numerous sharp results including coefficient estimate, distortion theorems, closure theorems, integral operators and linear combinations of several functions belonging to this class. We also obtain radii of close-to-convexity, starlikeness and convexity for functions belonging to A ∗ (p, A, B, α). Furthermore, various distortion inequalities for fractional calculus of functions in this class are given. Mathematics Subject Classification: Primary 30C45, Secondary 30C50