Pescar, "A new generalization of Ahlfors's and Becker's criterion of univalence
," Malaysian Mathematical Society (Second Series), vol.
Using this inequality, the bounds for the radius of univalence
, full starlikeness, and full convexity of order [alpha] (0 [less than or equal to] [alpha] < 1) are obtained for functions f = h + [bar.g] [member of] [H.sup.0.sub.sp] where the coefficients of the analytic part h satisfy one of the conditions [absolute value of [a.sub.n]] [less than or equal to] n, [absolute value of [a.sub.n]] [less than or equal to] 1, or [absolute value of [a.sub.n]] [less than or equal to] 1/n for n [greater than or equal to] 2.
All input share function, w/[f.sub.i](w) x [partial derivative][f.sup.i](w)/[partial derivative][w.sup.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.sup.l].sub.++].
Bulut, Sufficient conditions for univalence
of an integral operator defined by Al-Oboudi differential operator, J.
In this paper, our main aim is to study the convexity and univalence
of the integral operators
of Gaussian and confluent hypergeometric functions, Proc.
Thus, it is interesting to observe that many results on the univalence
property of integral operators follow the convexity property according to main results, especially Theorem 3 or Remark 4.
Livingston, On the radius of univalence
of certain analytic functions, Proc.
and convexity properties for confluent hypergeometric functions," Complex Variables, Theory and Application, vol.
problems in the class of typically real functions were considered by Golusin in .
Obradovic, "Simple sufficient conditions for univalence
," Matematichki Vesnik, vol.
Obradovic, Simple sufficient conditions for univalence