Applications of Symmetric Conic Domains to a Subclass of <i>q</i>-Starlike Functions

Abstract

In this paper, the theory of symmetric q-calculus and conic regions are used to define a new subclass of q-starlike functions involving a certain conic domain. By means of this newly defined domain, a new subclass of normalized analytic functions in the open unit disk E is given. Certain properties of this subclass, such as its structural formula, necessary and sufficient conditions, coefficient estimates, Fekete–Szegö problem, distortion inequalities, closure theorem and subordination results, are investigated. Some new and known consequences of our main results as corollaries are also highlighted.

Keywords

• quantum (or q-) calculus
• symmetric quantum (or q-) calculus
• symmetric q-derivative
• q-starlike functions
• symmetric conic domains