A Subclass of Analytic Functions Related to k-Uniformly Convex and Starlike Functions

We investigate some subclasses of k-uniformly convex and k-uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed.