In this paper, we introduce and investigate a new class of meromorphic functions defined by a differential operator. For this class, we obtain coefficient inequality, distortion inequality, radius of close-to-convex, starlikeness and convexity, extreme points and integral means inequality.

It is known that the ratio of Gaussian hypergeometric functions can be represented by means of g -fractions. In this work, the ratio of q -hypergeometric functions are represented by means of g -fractions that lead to certain results on q -starlikeness of the q -hypergeometric functions defined on the open unit disk. Corresponding results for the q -convex case are also obtained.

Abstract. The object of the present paper is to study certain subclasses J∗ p (a, b, σ) and Cp(a, b, σ) of analytic p-valent functions, and obtain coefficient bounds and distortion properties for functions belonging to these subclasses. Further results include distortion inequalities and radii of close-toconvexity, starlikeness and convexity for these classes of functions.

The main object of the present paper is to derive some results for multivalent analytic functions defined by a linear operators. As a special case of these results, we obtain several sufficient conditions for close-to-convexity and starlikeness of certain analytic functions.

The main object of this paper is to investigate and determine a sufficient condition for q-starlikeness q-convexity functions which are associated with normalized Gauss hypergeometric function.