Applications of a New <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>q</a:mi> </a:math>-Difference Operator in Janowski-Type Meromorphic Convex Functions

The main aim of the present article is the introduction of a new differential operator in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"> <a:mi>q</a:mi> </a:math> -analogue for meromorphic multivalent functions which are analytic in punctured open unit disc. A subclass of meromorphic multivalent convex functions is defined using this new differential operator in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M3"> <c:mi>q</c:mi> </c:math> -analogue. Furthermore, we discuss a number of useful geometric properties for the functions belonging to this class such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity. Also, algebraic property of closure is discussed of functions belonging to this class. Integral representation problem is also proved for these functions.