Geodesic
On a functional on the class of pairs of functions
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2013), pp. 44-56 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem about the range $\Delta$ of the functional $\Phi$ is solved by the method of internal variations on the class of pairs of functions univalent in the “disk–exterior of the disk” system. We have obtained a system of functional-differential equations for pairs of functions $(f(z),F(\zeta))\in\mathfrak M'$ that are in correspondence with nonsingular boundary points $\Phi_0$ of the set $\Delta$. Each equation from the system contains a parameter which is a root of an algebraic equation of the sixth degree.
Keywords: class $\mathfrak M'$, functional, range, boundary functions, differential equations. 
@article{VTGU_2013_2_a4,
     author = {V. A. Pchelintsev},
     title = {On a~functional on the class of pairs of functions},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {44--56},
     year = {2013},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2013_2_a4/}
}
TY  - JOUR
AU  - V. A. Pchelintsev
TI  - On a functional on the class of pairs of functions
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2013
SP  - 44
EP  - 56
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VTGU_2013_2_a4/
LA  - ru
ID  - VTGU_2013_2_a4
ER  - 
%0 Journal Article
%A V. A. Pchelintsev
%T On a functional on the class of pairs of functions
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2013
%P 44-56
%N 2
%U http://geodesic.mathdoc.fr/item/VTGU_2013_2_a4/
%G ru
%F VTGU_2013_2_a4
V. A. Pchelintsev. On a functional on the class of pairs of functions. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2013), pp. 44-56. http://geodesic.mathdoc.fr/item/VTGU_2013_2_a4/

[1] Aleksandrov I. A., “K voprosu o svyaznosti mnozhestva znachenii funktsionala”, Voprosy matematiki, Trudy Tomsk. gos. un-ta, 155, 1961, 72–76 | MR

[2] Aleksandrov I. A., Parametricheskie prodolzheniya v teorii odnolistnykh funktsii, Nauka, M., 1976 | MR

[3] Aleksandrov I. A., Metody geometricheskoi teorii analiticheskikh funktsii, Tom. gos. un-t, Tomsk, 2001

[4] Golubev V. V., Lektsii po analiticheskoi teorii differentsialnykh uravnenii, GITTL, M., 1950

[5] Goluzin G. M., “Metod variatsii v konformnom otobrazhenii. I”, Matem. sb., 19(61):2 (1946), 203–236 | MR | Zbl

[6] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR | Zbl

[7] Lebedev N. A., “Mazhorantnaya oblast dlya vyrazheniya $I=\ln\{z^\lambda[f'(z)]^{1-\lambda}/[f(z)]^\lambda\}$ v klasse $S$”, Vestn. Leningr. un-ta. Matem., fiz. i khim., 1955, no. 8(3), 29–41 | Zbl

[8] Matveev P. N., Lektsii po analiticheskoi teorii differentsialnykh uravnenii, Lan, SPb., 2008

[9] Pchelintsev V. A., “Ob odnoi ekstremalnoi zadache”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2012, no. 3(19), 22–30