Quantum calculus had been used first time by M.E.H.Ismail, E.Merkes and D.Steyr in the theory of univalent functions [5].In this present paper we examine the subclass of univalent functions which is defined by quantum calculus.

In the present paper, we introduce a new subclass of normalized analytic starlike functions by using bounded radius rotation associated with q- analogues in the open unit disc \mathbb D. We investigate growth theorem, radius of starlikeness and coefficient estimate for the new subclass of starlike functions by using bounded radius rotation associated with q- analogues denoted by \mathcal{R}_k(q), where k\geq2, q\in(0,1).

In the present paper, we study on the subclass of starlike functions of complex order with bounded radius rotation using q− difference operator denoted by R k (q, b) where k ≥ 2, q ∈ (0, 1) and b ∈ C\{0}. We investigate coefficient inequality, distortion theorem and radius of starlikeness for the class R k (q, b).2010 Mathematics Subject Classification. 30C45.

Abstract:In this paper, we obtain new extremal functions for starlike functions and convex functions on the rangedefined on the unit disk using analytic and univalent functions.

"We introduce a new subclass of Salagean-type harmonic multivalent functions by using q-diference operator. We investigate suficient coeficient estimates, distortion bounds, extreme points, convolution properties and neighborhood for the functions belonging to this function class."