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.