a function is said to be bi-univalent on the open unit disk d if both the function and its inverse are univalent in d. not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. in this paper we use the faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subord...

A function is said to be bi-univalent on the open unit disk D if both the function and its inverse are univalent in D. Not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. In this paper we use the Faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subord...

The theory of harmonic univalent mappings has become a very popular research topic in recent years. The aim of this expository article is to present a guided tour of the planar harmonic univalent and related mappings with emphasis on recent results and open problems and, in particular, to look at the harmonic analogues of the theory of analytic univalent functions in the unit disc.

The main purpose of this paper is to introduce a generalization of modified Salagean operator for harmonic univalent functions. We define a new subclass of complex-valued harmonic univalent functions by using this operator ,and we investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points and convex combination for the above class of harmonic univalent functi...

where (a) m is nonnegative integer, (b) β= a(0)(1+a(0))/(1−|a(0)|2) and therefore, β >−1/2, (c) h and g are analytic in U , g(0)= 1, and h(0)≠ 0. Univalent logharmonic mappings on the unit disc have been studied extensively. For details see [1, 2, 3, 4, 5, 6, 7, 8]. Suppose that f is a univalent logharmonic mapping defined on the unit disc U . Then, if f(0) = 0, the function F(ζ) = log(f (eζ)) ...

The main result shows that a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighbourhood consisting entirely of univalent functions. For the particular choice of a linear function in the hypothesis of the main theorem, we obtain a corollary which is equivalent to the classical Noshiro–Warschawski–Wolff univalence criterion. We also pr...

Ruscheweyh and Sheil-Small proved that convexity is preserved under the convolution of univalent analytic mappings in K. However, when we consider the convolution of univalent harmonic convex mappings in K H , this property does not hold. In fact, such convolutions may not be univalent. We establish some results concerning the convolution of univalent harmonic convex mappings provided that it i...

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...