Comprehensive subclasses of multivalent functions with negative coefficients defined by using a q-difference operator

Motivated by q-analogue theory, we define here q-analogue of p-valent Salagean differential operator. Then we introduce a new subclass of starlike and convex functions with negative coefficients, for which we obtain some properties such as coefficient estimates, distortion theorem, radii of starlikeness, convexity and close-to-convexity for functions belonging to these subclasses. Also, we introduce the modified-Hadamard product theorems. Finally, we give an application of the q-fractional calculus. (C) 2018 Ivane Javakhishvili Tbilisi State University. Published by Elsevier B.V.