# UNIVALENCE PROPERTIES FOR A GENERAL INTEGRAL OPERATOR

• Breaz, Daniel
• Published : 2009.05.31
• 57 8

#### Abstract

We consider the univalence function classes T, $T_2,\;T_{2,{\mu}}$, and S(p). For these classes we shall study some univalence properties for a general integral operator. Furthermore we shall extend some known univalence criteria, i.e., Becker-type criteria.

#### Keywords

analytic functions;integral operator;univalent function;Supported by the GAR 19/2008

#### References

1. L. V. Ahlfors, Sufficient conditions for quasiconformal extension, Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973), pp. 23–29. Ann. of Math. Studies, No. 79, Princeton Univ. Press, Princeton, N.J., 1974
2. J. Becker, Lownersche Differentialgleichung und Schlichtheitskriterien, Math. Ann. 202 (1973), 321–335 https://doi.org/10.1007/BF01433462
3. D. Breaz and N. Breaz, The univalent condition for an integral operator on the classes S($\alpha) and T_2$, Acta Univ. Apulensis Math. Inform. No. 9 (2005), 63–69
4. Z. Nehari, Conformal Mapping, McGraw-Hill Book Co., Inc., New York, Toronto, London, 1952
5. S. Ozaki and M. Nunokawa, The Schwarzian derivative and univalent functions, Proc. Amer. Math. Soc. 33 (1972), 392–394
6. V. Pescar, A new generalization of Ahlfors's and Becker's criterion of univalence, Bull. Malaysian Math. Soc. (2) 19 (1996), no. 2, 53–54
7. D. Breaz and H. O. Guney, On the univalence criterion of a general integral operator, J. Inequal. Appl. 2008 (2008), Art. ID 702715, 8 pp https://doi.org/10.1155/2008/702715

#### Cited by

1. On certain general integral operators of analytic functions vol.66, pp.1, 2012, https://doi.org/10.2478/v10062-012-0003-3
2. On a Certain Integral Operator vol.52, pp.1, 2012, https://doi.org/10.5666/KMJ.2012.52.1.33