Abstract:
Using two methods, quasiconformal continuation involving a theorem of Hadamard and direct estimation of f(z2)−f(z1), we obtain sufficient conditions for the univalence of continuously differentiable mappings f(z) of plane domains which, in the case of conformal mappings, reduce to both well-known and new results.
Citation:
F. G. Avkhadiev, “Sufficient conditions for the univalence of quasiconformal mappings”, Mat. Zametki, 18:6 (1975), 793–802; Math. Notes, 18:6 (1975), 1063–1067
This publication is cited in the following 4 articles:
R. G. Nasibullin, I. K. Shafigullin, “Avkhadiev–Becker type multivalence conditions for harmonic mappings of a disc”, Russian Math. (Iz. VUZ), 61:3 (2017), 72–76
F. G. Avkhadiev, P. L. Shabalin, “Conformal mappings of circular domains on finitely-connected non-Smirnov type domains”, Ufa Math. J., 9:1 (2017), 3–17
F. G. Avkhadiev, “On locally invertible harmonic mappings of plane domains”, Lobachevskii J Math, 38:3 (2017), 400
F. G. Avkhadiev, R. G. Nasibullin, I. K. Shafigullin, “Becker type univalence conditions for harmonic mappings”, Russian Math. (Iz. VUZ), 60:11 (2016), 69–73