Abstract
UDC 517.5
We give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker’s method. Further, new univalence criteria and the significant relationships with other results are given. A number of known univalence conditions would follow upon specializing the parameters involved in main results.
Publisher
Institute of Mathematics National Academy of Sciences of Ukraine
Reference36 articles.
1. L. V. Ahlfors, Sufficient conditions for quasiconformal extension, Ann. Math. Stud., 79, 23 – 29 (1974).
2. J. M. Anderson, A. Hinkkanen, Univalence criteria and quasiconformal extensions, Trans. Amer. Math. Soc., 324, № 2, 823 – 842 (1991); https://doi.org/10.2307/2001743
3. J. Becker, L¨ownersche Differential gleichung und quasikonform fortsetzbare schlichte Funktionen, J. reine angew. und Math., 255, 23 – 43 (1972); https://doi.org/10.1515/crll.1972.255.23
4. J. Becker, Über die Lösungsstruktur einer Differentialgleichung in der konformen Abbildung (German) , J. reine und angew. Math., 285, 66 – 74 (1976); https://doi.org/10.1515/crll.1976.285.66
5. J. Becker, Conformal mappings with quasiconformal extensions, Aspects of Contemporary Complex Analysis, Acad.Press (1980), p. 37 – 77.