On a New Subclass of <i>q</i>-Starlike Functions Defined in <i>q</i>-Symmetric Calculus

Abstract

Geometric function theory combines geometric tools and their applications for information and communication analysis. It is also successfully used in the field of advanced signals, image processing, machine learning, speech and sound recognition. Various new subclasses of analytic functions have been defined using quantum calculus to investigate many interesting properties of these subclasses. This article defines a new class of q-starlike functions in the open symmetric unit disc ∇ using symmetric quantum calculus. Extreme points for this class as well as coefficient estimates and closure theorems have been investigated. By fixing several coefficients finitely, all results were generalized into families of analytic functions.

Keywords

• univalent function
• starlike function
• uniformly convex function
• q-starlike function
• q-symmetric derivative operator