Coefficient inequalities for certain classes of multivalent functions of complex order defined by multiplier operator

Abstract

In this paper, we first define the multiplier operator }$\mathcal{J}${\small $_{c,p,\lambda }^{m,\delta }$ in terms of Komatu integral operator. Then we define new classes of $p-$% valent starlike and convex functions with complex order. The main object is to obtain coefficient inequalities for functions belonging to the newly defined classes. Also we get coefficient inequalities for functions in certain subclass satisfying a nonhomogeneous Cauchy-Euler differential equation. Several particular results (known or new) of the main theorems are mentioned.