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.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference26 articles.
1. On subclasses of uniformly convex functions and corresponding class of starlike functions;Bharati;Tamkang J. Math.,1997
2. Subclasses of k-uniformly convex and starlike functions defined by generalized derivate;Kanas;Indian J. Pure Appl. Math.,2001
3. On uniformly starlike functions;Goodman;J. Math. Anal. Appl.,1991
4. A survey on uniformly convex and uniformly starlike function;Ann. Univ. Mariae Curie-Sklodowska.,1993
5. Subclasses of analytic functions defined by a new differential operator;Deniz;Acta. Uni. Apul.,2014