The aim of this paper is two-fold. First, to give a direct proof for the already established result of Styer which states that a univalent geometrically starlike function f is a univalent annular starlike function if f is bounded. Second, to show that the boundedness condition of f is necessary, thus disproving a conjecture of Styer.

1 Presented by We construct a function f (z), univalent and starlike in the unit disc, with some interesting geometric and analytic properties. It turns out that its convolutions f * λn with a specific class of univalent polynomials λn(z) are not subordinate to the function itself. This provides a counterexample to a result of Greiner and Ruscheweyh.

The rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. The rational bi-cubic function involves six parameters in each rectangular patch. Data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

The purpose of this work is to present a class harmonic univalent functions de?ned by the Dziok-Srivastava operator. Some geometric properties like coefficients conditions, distortion theorem, convolution (Hadamard product), convex combination and extreme points are investigated.
 2000 Mathematics Subject Classi?cation: 30C45, 30C50

In this work, the subclass of the function class S of analytic and bi-univalent functions is defined and studied in the open unit disc. Estimates for initial coefficients of Taylor- Maclaurin series of bi-univalent functions belonging these class are obtained. By choosing the special values for parameters and functions it is shown that the class reduces to several earlier known classes of analy...

FMN and flavodoxin, when reduced by the action of ferredoxin-TPN+ oxidoreductase, have been shown to cause both univalent and divalent reductions of oxygen. Superoxide radicals, so generated, were detected by their abilities to oxidize epinephrine to adrenochrome and to reduce cytochrome c. Superoxide dismutase inhibited these actions of the superoxide radical. The ratio of the univalent reduct...