In the present work, authors introduce a new linear differential operator associated with $ q $-calculus which uses $-derivative operator. For class involving operator, interesting properties like coefficient inequality, growth, distortion, convolution and radii of starlikeness are established. Various connections that earlier works pointed out.

Let denote the functions' class that is normalized, analytic, as well univalent in unit disc given by src=image/13426735_01.gif>. Convex, starlike, close-to-convex functions resemble main subclasses of src=image/13426735_02.gif>, expressed src=image/13426735_03.gif>, src=image/13426735_04.gif>, accordingly. Many mathematicians have recently studied radius problem...

In the present paper, our aim is to study geometric properties of normalized Rabotnov functions. For this purpose, we determined sufficient conditions for univalency, close-to-convexity, convexity and starlikeness functions in open unit disk.

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means a q-difference operator. Some properties the in this subclass, such as sufficient and necessary conditions, coefficient estimates, growth distortion theorems, radius starlikeness convexity, partial sums closure are investigated.