Keywords: Operator Hadamard product Bazilevic functions Starlike functions Hypergeometric functions p-valent functions a b s t r a c t Let AðpÞ; p 2 N, be a class of functions f : f ðzÞ ¼ z p þ P 1 k¼pþn a k z k analytic in the open unit disc E. We use Carlson–Shaffer operator for p-valent functions to define and study certain classes of analytic functions. Inclusion results, a radius problem a...

In this paper, we define a generalized class of starlike functions with negative coefficients and obtain coefficient estimates, distortion bounds, closure theorems and extreme points. Further we obtain modified Hadamard product, radii of close-to-convex, starlikeness and convexity for functions belonging to this class. Furthermore neighborhood results are discussed.

In this paper we study functions which are strongly starlike, with the method of differential inequalities. We also give a generalization of the results obtained by the authors Milutin Obradovic and Santosh B. Joshi (1998) with new class of functions defined by q order ordinary differential operator.

A comprehensive class of complex-valued harmonic prestarlike univalent functions is introduced. Necessary and sufficient coefficient bounds are given for functions in this class to be starlike. Distortion bounds and extreme points are also obtained. 2000 Mathematics Subject Classification:Primary 30C45, 30C50.

For a constant k ∈ [0,∞) a normalized function f , analytic in the unit disk, is said to be k-uniformly convex if Re (1 + zf ′′(z)/f ′(z)) > k|zf ′′(z)/f ′(z)| at any point in the unit disk. The class of k-uniformly convex functions is denoted k-UCV (cf. [4]). The function g is said to be k-starlike if g(z) = zf ′(z) and f ∈ k-UCV. For analytic functions f, g, where f(z) = z + a2z + · · · and g...

Making use of Linear operator theory, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain coefficient estimates distortion bounds, closure theorems and extreme points for functions belonging to this new class. The results are generalized to families with fixed finitely ma...