Fractional Calculus Operators Associated with a Subclass of Uniformly Convex Functions

Abstract

Making use of fractional calculus operator, we define a new subclass of uniformly convex functions with negative coefficients. Characterization property, extreme points, distortion bounds, the results on Integral transform and sharp integral means inequalities for the function class are determined.

Key words and phrases. Classes of Univalent functions, convex functions, starlike functions, uniformly convex functions, fractional derivatives, fractional integral, integral means.

1991 Mathematics Subject Classification. Primary: 30C45; Secondary: 30C50