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...

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)) ...

Let be the class of functions which are analytic in open unit disk and having form . Denote to for all that univalent Then, let denote bi-univalent In this paper, we obtain second Hankel determinant certain classes function defined by subordinations particular, determine initial coefficients obtained upper bound functional

Let f be a sense-preserving harmonic mapping in the unit disk. We give a sufficient condition in terms of the pre-Schwarzian derivative of f to ensure that it can be extended to a quasiconformal map in the complex plane. Introduction A well-known criterion due to Becker [5] states that if a locally univalent analytic function φ in the unit disk D satisfies (1) sup z∈D ∣∣∣∣φ′′(z) φ′(z) ∣∣∣∣ (1− ...

We define a new subclass of univalent function based on Salagean differential operator and obtained the initial Taylor coefficients using the techniques of Briot-Bouquet differential subordination in association with the modified sigmoid function. Further we obtain the classical Fekete-Szego inequality results.

The main aim of this paper is to use the method of differential subordination to obtain a number of sufficient conditions for a normalized analytic function to be univalent or starlike in the unit disc. In particular, we find a condition on β so that each normalized analytic function f satisfying the condition ∣∣∣1 + zf ′′(z) 2f ′(z) − zf ′(z) f(z) ∣∣∣ < β, z ∈ Δ implies that f is univalent or ...

For r > 0 let r {z ∈ : |z| < r}. Let 1 . Let the functions f and F be analytic in the unit disc . A function f is called subordinate to F, written f ≺ F, if F is univalent in , f 0 F 0 and f ⊂ F . Let D be a domain in 2 and ψ : 2 ⊃ D → be an analytic function, and let p be a function analytic in with p z , zp′ z ∈ D, z ∈ and h be a function analytic and univalent in . The function p is said to ...

Since the function z 7→ 1+z 1−z is univalent with image the right half plane, we see that z 7→ ( 1+z 1−z )2 is univalent, so k ∈ S, and the image of k is the entire complex plane except for real numbers ≤ −14 . In 1916, L. Bieberbach [Bi] conjectured that the Koebe function was maximal with respect to the absolute value of the coefficients of its power series. More precisely, he conjectured the...