On Quantum Differential Subordination Related with Certain Family of Analytic Functions

Recently, there is a rapid increase of research in the area of Quantum calculus (known as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>q</a:mi> </a:math> -calculus) due to its widespread applications in many areas of study, such as geometric functions theory. To this end, using the concept of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>q</c:mi> </c:math> -conic domains of Janowski type as well as <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"> <e:mi>q</e:mi> </e:math> - calculus, new subclasses of analytic functions are introduced. This family of functions extends the notion of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M4"> <g:mi>α</g:mi> </g:math> -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.