On neighborhoods of univalent convex functions

Some Sharp Neighborhoods of Univalent Functions

For 5 > 0 and /(z) = z + a2z2 + ••■ analytic in \z\ < 1 let the 5neighborhood of/, Ns(f), consist of those analytic functions g(z) — z + b2z2 + ••• with E"_2 k\ak bk\ < S. We determine sufficient conditions guaranteeing which neighborhoods of certain classes of convex functions belong to certain classes of starlike functions. We extend some recent results of St. Ruscheweyh and R. Fournier and, ...

Convex and Starlike Univalent Functions

Generating Starlike and Convex Univalent Functions

Alexander [1] was the first to introduce certain subclasses of univalent functions examining the geometric properties of the image f(D) of D under f . The convex functions are those that map D onto a convex set. A function w = f(z) is said to be starlike if, together with any of its points w, the image f(D) contains the entire segment {tw : 0 ≤ t ≤ 1}. Thus we introduce the denotations S = {f ∈...

On a Subclass of Quasi-Convex Univalent Functions

Abstract: The aim of this paper is to introduce and study a new class [ ] * C A,B, δ α of Janowski QuasiConvex univalent functions of order alpha associated with Ruscheweyh derivative. Sharp coefficient bound, distortion result and some inclusion results are discussed. Invariance of [ ] * C A,B, δ α under convolution with convex functions has also been examined and some of its applications are ...

Subclasses of Univalent Functions Subordinate to Convex Functions

In this paper, we define a new subclass Ao(A, B) of univalent functions and investigate several interesting characterization theorems involving a general class S" [A, B] of starlike functions