G. Murugusundaramoorthy, S. Sivasubramanian, R. K. Raina Abstract. The authors introduce a new subclass UH(α, β, γ, δ, λ, k) of functions which are analytic in the open disc ∆ = {z ∈ C : |z| < 1}. Various results studied include the coefficient estimates and distortion bounds, radii of close-to-convexity, starlikeness and convexity and integral means inequalities for functions belonging to the ...

Abstract. The object of this paper is to show some properties of functions belonging to a subclass Mp(A, B, b, n) (where b is a complex number with Re(b) > 0 and A and B are two arbitrary constants with −1 6 B < A 6 1). Coefficient estimates and some distortion theorems for this class of functions are found. Radii of close-to-convexity, starlikeness and convexity are derived. An application to ...

Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the class TSm α, β, γ . In particular, we obtain integral means ineq...

In the present investigation, we obtain certain sufficient conditions for a normalized analytic function f(z) defined by the Dziok–Srivastava linear operator Hm1⁄2a1 to satisfy the certain subordination. Our results extend corresponding previously known results on starlikeness, convexity, and close to convexity. 2006 Elsevier Inc. All rights reserved.

Abstract. By making use of the generalized hypergeometric functions, in this paper we introduce and investigate certain new subclasses of analytic functions of complex order defined in the open unit disk. Coefficient inequalities, radii of close-to-convexity, starlikeness and convexity, closure theorems, integral means inequalities and several relations associated with (n, δ)-neighborhood for t...

In the present paper, we consider the subclass of meromorphic univalent functions S∗ p [k, α, β, c] with fixed second positive coefficient. The object of the present paper is to show coefficient estimates, convex liner combinations, some distortion theorems, and redii of starlikeness and convexity for f(z) in the class S∗ p [k, α, β, c].

In this paper we introduce new subclasses of k-uniformly convex and starlike functions with respect to other points. We provide necessary and sufficient conditions, coefficient estimates, distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity for these classes. We also obtain integral means inequalities with the extremal functions for these classes.

By introducing a new subcalss of p-valent functions with respect to (j, k)-symmetric points, we have obtained the integral representations and conditions for starlikeness by using differential subordination. Some already known results have been, incidentally, shown to be particular cases of the main results of the paper.

We obtain a sufficient condition for starlikeness of orderα, |f ′(z)−λ(f(z)/z)+ λ−1|<M =Mn(λ,α), where λ∈ [0,1], α∈ [0,1) and the function f(z)= z+an+1zn+1+ ··· is analytic in the unit disc U . 2000 Mathematics Subject Classification. 30C45.

In this paper we introduce and study some properties of a unified class U [μ, α, β, γ, λ, η, A,B] of prestarlike functions with negative coefficients in a unit disk U . These properties include growth and distortion, radii of convexity, radii of starlikeness and radii of close-to-convexity.