We will give the relation between the class of Janowski starlike functions of complex order and the class of Janowski convex functions of complex order. As a corollary of this relation, we obtain the radius of starlikeness for the class of Janowski convex functions of complex order. 1. Introduction. Let F be the class of analytic functions in D = {z | |z| < 1}, and let S denote those functions ...

We introduce new classes of q -starlike and q -convex functions of complex order involving the q -derivative operator defined in the open unit disc. Furthermore, we find estimates on the coefficients for second and third coefficients of these classes.

For p-valently Janowski starlike and convex functions defined by applying subordination for the generalized Janowski function, the sharp upper bounds of a functional |a p2 − μa 2 p1 | related to the Fekete-Szegö problem are given.

Many mathematical concepts are explained when viewed through complex function theory. We here basically concerned with the form f(z)=a0+a1z+a2z2+...f(z) ?A, f(z)=z+??, n=2anZ2 will be an analytic in open unit disc U={z:|z|&lt;1, z=?C}normalized by f(0) = 0, f'(0)=1. In this work, starlike functions and close-to-convex order 1/4 have been studied according to exact requirements.