Applications on a subclass of β-uniformly starlike functions connected with q-Borel distribution

The aim of this paper is to define the operator of [Formula: see text]-derivative based upon the Borel distribution and by using this operator, we familiarize a new subclass of [Formula: see text]-uniformly starlike functions [Formula: see text]-[Formula: see text] Further, we obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-to-convexity, starlikeness and convexity for functions [Formula: see text]-[Formula: see text] We also determine the second Hankel inequality for functions belonging to this subclass.

Mapping properties of certain linear operator associated with hypergeometric functions

The main object of the present paper is to nd some su¢ cient conditions in terms of hypergeometric inequalities so that the linear operator denoted by Ha;b;c : maps a certain subclass of close-to-convex function R (A;B) into subclasses of k-uniformly starlike and k-uniformly convex functions k 􀀀ST () and k 􀀀UCV() respectively. Further, we consider an integral operator and discuss its properties. Our results generalize some relevant results.

A Subclass of Analytic Functions Related tok-Uniformly Convex and Starlike Functions

We investigate some subclasses ofk-uniformly convex andk-uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed.