On certain multivalent functions with negative coefficients defined by using a differential operator

Abstract

In this paper, we introduce the subclass $S_{j}(n,p,q,\alpha)$ of analyticand $p$-valent functions with negative coefficients defined by new operator $D_{p}^{n}$. In this paper we give some properties of functions in the class $S_{j}(n,p,q,\alpha)$ and obtain numerous sharp results including (forexample) coefficient estimates, distortion theorem, radii ofclose-to-convexity, starlikeness and convexity and modified Hadamardproducts of functions belonging to the class $S_{j}(n,p,q,\alpha)$.Finally, several applications involving an integral operator and certainfractional calculus operators are also considered.