Generalization of certain subclasses of multivalent functions with negative coefficients defined by using a differential operator

Abstract

Making use of a differential operator, we introduce and study a certain class S C n ( j , p , q , α , λ ) of p -valently analytic functions with negative coefficients. In this paper, we obtain numerous sharp results including (for example ) coefficient estimates, distortion theorem, radii of close-to convexity, starlikeness and convexity and modified Hadamard products of functions belonging to the class S C n ( j , p , q , α , λ ) . Finally, several applications investigate an integral operator, and certain fractional calculus operators are also considered.