On Quantum Differential Subordination Related with Certain Family of Analytic Functions

Abstract

Recently, there is a rapid increase of research in the area of Quantum calculus (known as $q$ -calculus) due to its widespread applications in many areas of study, such as geometric functions theory. To this end, using the concept of $q$ -conic domains of Janowski type as well as $q$ - calculus, new subclasses of analytic functions are introduced. This family of functions extends the notion of $\alpha$ -convex and quasi-convex functions. Furthermore, a coefficient inequality, sufficiency criteria, and covering results for these novel classes are derived. Besides, some remarkable consequences of our investigation are highlighted.