and convexity properties for confluent hypergeometric functions, Complex Variables Theory Appl.
j], that matters is that the determinant of the function be uniformly bounded away from zero in order to attain global univalence
within the strictly positive orthant, [[R.
Guney, On the univalence
criterion of a general integral operator, J.
TTze radius of univalence
of the function F given by (1) z's ajzzaZ to [square root of (3)]/ 3.
AKSENTEV: Sufficient conditions for univalence
of regular functions (Russian), Izv.
For [beta] = 0, this latter condition is sufficient for the close-to-convexity and hence univalence
of the function f.
LU](A)) is called the radius of univalence
) in the class A, if it is the maximum of numbers r [member of] (0,1], such that every function f [member of] A is univalent (local univalent) in [absolute value of z] < r.
Nehari showed that the univalence
of an analytic function in D can be guaranteed if its Schwarzian derivative is dominated by a suitable positive function [10, Theorem I, p.
Jahangiri, Coefficient bounds and univalence
criteria for harmonic functions with negative coefficients, Ann.
Livingston,: On the radius of univalence
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r], r [member of] (0,1) we need to know the set of univalence
, or at least the radius of univalence
, for H.
the condition for univalence
in Theorem 6 is satisfied and so, f [member of] [S.