On Subclass of k -Uniformly Convex Functions of Complex Order Involving Multiplier Transformations

Abstract

We introduce a subclass of $k$-uniformly convex functions of order $\alpha$ with negative coefficients by using the multiplier transformations in the open unit disk . We obtain coefficient estimates, radii of convexity and close-to-convexity, extreme points, and integral means inequalities for the function $f$ that belongs to the class ${\mathcal{N}}_m^{\mathcal{l}}\left(\alpha ,\beta ,k,\upsilon \right)$.