Applications of fractional calculus to k-uniformly starlike and k-uniformly convex functions of order α

Abstract

A new subclass of analytic functions k - SPλ(α) is introduced by applying certain operators of fractional calculus to k-uniformly starlike and k-uniformly convex functions of order α. Some theorems on coefficient bounds and growth and distortion theorems for this subclass are found. The radii of close to convexity, starlikeness and convexity for this subclass is also derived.