.z I < p(e), E < p(E) < Po, and p(c) depends not only on e but also on w(z). The function p(E) clearly decreases monotonically with e; it also approaches zero with e, for the transformation z(w), although multiple-valued, is continuous. If now E(e) lies in Jz < E, E < Eo, then the convex hull of w(E(e)) contains the point w+, and the m antecedents z+ of w+ in jz < Po defined by equation (5) lie...

Clostridial and spinach ferredoxins, reduced enzymatically by the action of ferredoxin-TPN+ oxidoreductase, have been shown to carry out the univalent reduction of oxygen. The superoxide radicals, so generated, were detected by their ability to cause the oxidation of epinephrine to adrenochrome. Superoxide dismutase prevented the production of adrenochrome in these reaction mixtures, while havi...

We consider two parametric families of special functions: One is defined by a power series generalizing the classical Mathieu series, and other one generalized type involving factorials in its coefficients. Using criteria due to Fejér Ozaki, we provide sufficient conditions for these functions be close-to-convex or starlike inside unit disk, thus univalent. our proofs assisted symbolic computat...

In the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.

by using generalized salagean differential operator a newclass of univalent holomorphic functions with fixed finitely manycoefficients is defined. coefficient estimates, extreme points,arithmetic mean, and weighted mean properties are investigated.

Let f and F be members of . The function f is said to be subordinate to F, or F is said to be superordinate to f , if there exists a function w analytic in U, with w(0)= 0 and |w(z)| < 1, and such that f (z)= F(w(z)). In such a case, we write f ≺ F or f (z)≺ F(z). If the function F is univalent in U, then f ≺ F if and only if f (0)= F(0) and f (U)⊂ F(U) (cf. [1, 2]). Let φ : C2 → C and let h be...

Harmonic univalent mappings have attracted the serious attention of complex analysts only after the appearance of a basic paper by Clunie and Sheil-Small [4] in 1984. These researchers laid the foundation for the study of harmonic univalent mappings over the unit disk as a generalization of analytic univalent functions. Interestingly, almost at the same time, the famous Bieberbach conjecture wh...