sufficient conditions for univalence and starlikeness

Sufficient conditions for univalence and starlikeness

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

Some Sufficient Conditions for Univalence and Starlikeness

The object of the present paper is to derive certain sufficient conditions for univalence, p-valently starlikeness and p-valently close-to-convexity of analytic functions in the unit disk. Our results extend and improve some results due to Owa [3], Frasin and Darus [2] and Chen [1].

Sufficient Conditions for Janowski Starlikeness

Let A,B,D,E ∈ [−1,1] and let p(z) be an analytic function defined on the open unit disk, p(0) = 1. Conditions on A, B, D, and E are determined so that 1 + βzp′(z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz). Similar results are obtained by considering the expressions 1 + β(zp′(z)/p(z)) and 1 + β(zp′(z)/p2(z)). These results are then applied to obtain s...

Some Sufficient Conditions for Univalence

A new subclass R(u), 0 < u < I, of the class St(I/2) the class of starlike functions of order I/2 is introduced and it is shown that R(u) is closed with respect to the Hadamard product of analytic functions. Some sufficient conditions for the normalized regular functions to be univalent in the unit disk E are given.

On Certain Sufficient Conditions for Starlikeness

We consider certain properties of f(z)f ′′(z)/f ′2(z) as a sufficient condition for starlikeness.

SUFFICIENT CONDITIONS FOR UNIVALENCE IN Cn