Abstract:
In the first part of the paper there is given a survey of the contemporary state of the theory of the sufficient univalence and $p$-valence conditions for analytic and meromorphic functions of a complex variable. The second part is devoted to a survey of the results on the conditions for the univalent solvability of applied inverse boundary value problems.
Citation:
F. G. Avkhadiev, L. A. Aksent'ev, A. M. Elizarov, “Sufficient conditions for the finite-valence of analytic functions, and their applications”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 25, VINITI, Moscow, 1987, 3–121; J. Soviet Math., 49:1 (1990), 715–799
\Bibitem{AvkAksEli87}
\by F.~G.~Avkhadiev, L.~A.~Aksent'ev, A.~M.~Elizarov
\paper Sufficient conditions for the finite-valence of analytic functions, and their applications
\serial Itogi Nauki i Tekhn. Ser. Mat. Anal.
\yr 1987
\vol 25
\pages 3--121
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intm79}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=921051}
\zmath{https://zbmath.org/?q=an:0632.30019|0711.30017}
\transl
\jour J. Soviet Math.
\yr 1990
\vol 49
\issue 1
\pages 715--799
\crossref{https://doi.org/10.1007/BF02207024}
Linking options:
https://www.mathnet.ru/eng/intm79
https://www.mathnet.ru/eng/intm/v25/p3
This publication is cited in the following 12 articles:
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R. G. Nasibullin, “Hardy-type inequalities for the Jacobi weight with applications”, Siberian Math. J., 63:6 (2022), 1121–1139
R. G. Nasibullin, “One-dimensional $L_p$-Hardy-type inequalities
for special weight functions and their applications”, Ufa Math. J., 14:3 (2022), 97–116
A. V. Kazantsev, M. I. Kinder, “Avkhadiev–Lehto type constants in the study of the Gakhov class”, Russian Math. (Iz. VUZ), 65:3 (2021), 43–50
O. S. Kudryavtseva, A. P. Solodov, “Asymptotically sharp two-sided estimate for domains of univalence of holomorphic self-maps of a disc with an invariant diameter”, Sb. Math., 211:11 (2020), 1592–1611
L. A. Aksent'ev, A. I. Aptekarev, A. M. Bikchentaev, V. V. Goryainov, V. N. Dubinin, A. M. Elizarov, I. R. Kayumov, A. Laptev, S. R. Nasyrov, D. V. Prokhorov, A. G. Sergeev, V. D. Stepanov, “Farit Gabidinovich Avkhadiev (on his 70th birthday)”, Russian Math. Surveys, 73:1 (2018), 181–185
A. V. Kazantsev, “O vykhode iz mnozhestva Gakhova po semeistvu klassov Avkhadieva”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 159, no. 3, Izd-vo Kazanskogo un-ta, Kazan, 2017, 318–326
Denisa Fericean, “Strongly Φ-like functions of order α in two-dimensional free boundary problems”, Applied Mathematics and Computation, 218:15 (2012), 7856
S. R. Nasyrov, I. Z. Faizov, “Lokalnaya edinstvennost resheniya smeshannoi obratnoi kraevoi zadachi na poligonalnykh rimanovykh poverkhnostyakh s prostymi tochkami vetvleniya”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 148, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2006, 97–108
I. R. Kayumov, Yu. V. Obnosov, “Estimates for integral means of hyperbolically convex functions”, Siberian Math. J., 46:6 (2005), 1062–1068
I. R. Nezhmetdinov, “On the Univalence of an Integral on Subclasses of Meromorphic Functions”, Math. Notes, 69:1 (2001), 81–87
F. Kh. Arslanov, “K dostatochnym usloviyam odnolistnosti i edinstvennosti reshenii obratnykh kraevykh zadach”, Konstr. teor. funkts. i funkts. anal., 7, Izd-vo Kazanskogo un-ta, Kazan, 1990, 3–13
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