Sufficient Conditions for Univalence of an Integral Operator

Sufficient Conditions for Univalence of an Integral Operator Defined by Al-Oboudi Differential Operator

Univalence conditions for a general integral operator

For analytic functions in the open unit disk U , we define a new general integral operator. The main object of the this paper is to study this new integral operator and to determine univalence conditions of it. Several corollaries of the main results are also considered.

Sufficient conditions for univalence and starlikeness

It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $|z|

On the univalence of an integral operator

Let U = {z ∈ C : |z| < 1} be the unit disk in the complex plane, and let A be the class of functions which are analytic in the unit disk normalized with f (0) = f ′ (0)− 1 = 0. We denote by P the class of the functions p which are analytic in U , p (0) = 1 and Re p (z) > 0, for all z ∈ U . Let S be the subclass of A, consisting of all univalent functions f in U , and we consider S∗ the subclass...

The univalence conditions for a general integral operator

For analytic functions in the open unit disk, J. Becker (Math. Ann. 202(1973)) has given some univalent conditions. In the present paper, some extensions of Becker’s type are considered.