Subclasses of Uniformly Convex Functions with Negative Coefficients Based on Deniz–Özkan Differential Operator

Abstract

We introduce in this paper a new family of uniformly convex functions related to the Deniz–Özkan differential operator. By using this family of functions with a negative coefficient, we obtain coefficient estimates, the radius of starlikeness, convexity, and close-to-convexity, and we find their extreme points. Moreover, the neighborhood, partial sums, and integral means of functions for this new family are studied.

Keywords

• parabolic starlike
• neighborhood
• partial sum
• coefficient estimates
• uniformly convex
• differential operator