On convolution, convex, and starlike mappings

Some Results on Starlike and Convex Functions

Let A denotes the class of functions f(z) that are analytic in the unit disk U = {z : |z| < 1} and normalized by f(0) = f ′(0)− 1 = 0. Further, let f, g ∈ A. Then we say that f(z) is subordinate to g(z), and we write f(z) ≺ g(z), if there exists a function ω(z), analytic in the unit disk U , such that ω(0) = 0, |ω(z)| < 1 and f(z) = g(ω(z)) for all z ∈ U . Specially, if g(z) is univalent in U t...

Certain Subclasses of Uniformly Starlike and Convex Functions Defined by Convolution

Abstract. The aim of this paper is to obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-toconvexity, starlikeness and convexity for functions belonging to the subclass TSγ(f, g; α, β) of uniformly starlike and convex functions, we consider integral operators associated with functions in this class. Furthermore partial sums fn(z) of functions f(z) i...

Certain Subclasses of Strongly Starlike and Strongly Convex Functions Defined by Convolution

In the present paper certain subclasses of strongly starlike and strongly convex functions defined by convolution with the generalized Hurwitz -Lerch Zeta function are investigated. Some inclusion relations are also mentioned as special cases of our main results.

STABILITY OF THE INTEGRAL CONVOLUTION OF k-UNIFORMLY CONVEX AND k-STARLIKE FUNCTIONS

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...

Convex and Starlike Univalent Functions