On equivalent norms in the theory of Volterra polinomial equations of the first kind
The Bulletin of Irkutsk State University. Series Mathematics, Tome 3 (2010) no. 1, pp. 19-29 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper suggests a method for construction of equivalent norms in studies on existence of local continuous solutions of the Volterra polynomial integral equations of the fist kind. The method is based on solution of the majorant Cauchy problems.
Keywords: majorant integral equations; majorant Cauchy problems; contraction mapping; Lambert function.
@article{IIGUM_2010_3_1_a1,
     author = {A. S. Apartsyn},
     title = {On equivalent norms in the theory of {Volterra} polinomial equations of the first kind},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {19--29},
     year = {2010},
     volume = {3},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2010_3_1_a1/}
}
TY  - JOUR
AU  - A. S. Apartsyn
TI  - On equivalent norms in the theory of Volterra polinomial equations of the first kind
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2010
SP  - 19
EP  - 29
VL  - 3
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2010_3_1_a1/
LA  - ru
ID  - IIGUM_2010_3_1_a1
ER  - 
%0 Journal Article
%A A. S. Apartsyn
%T On equivalent norms in the theory of Volterra polinomial equations of the first kind
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2010
%P 19-29
%V 3
%N 1
%U http://geodesic.mathdoc.fr/item/IIGUM_2010_3_1_a1/
%G ru
%F IIGUM_2010_3_1_a1
A. S. Apartsyn. On equivalent norms in the theory of Volterra polinomial equations of the first kind. The Bulletin of Irkutsk State University. Series Mathematics, Tome 3 (2010) no. 1, pp. 19-29. http://geodesic.mathdoc.fr/item/IIGUM_2010_3_1_a1/

[1] V. A. Trenogin, Funktsionalnyi analiz, Nauka, M., 1980, 495 pp. | MR | Zbl

[2] M. A. Krasnoselskii i dr., Priblizhennoe reshenie operatornykh uravnenii, Nauka, M., 1969, 456 pp. | MR

[3] V. Khatson, Dzh. Pim, Prilozheniya funktsionalnogo analiza i teorii operatorov, Mir, M., 1983, 431 pp. | MR

[4] A. S. Apartsin, “O polilineinykh uravneniyakh Volterra I roda”, Avtomatika i telemekhanika, 2004, no. 2, 118–125 | MR

[5] A. S. Apartsin, “Polilineinye integralnye uravneniya Volterra I roda: elementy teorii i chislennye metody”, Izv. Irkut. gos. un-ta. Ser.: Matematika, 2007, no. 1, 13–41

[6] A. S. Apartsin, “Polilineinye uravneniya Volterra I roda i nekotorye zadachi upravleniya”, Avtomatika i telemekhanika, 2008, no. 4, 3–16 | MR | Zbl

[7] A. S. Apartsyn, “Unimprovable estimates of solutions for some classes integral inequalities”, Inverse and Ill-posed Problems, 16:7 (2008), 561–590 | MR

[8] A. S. Apartsin, Neklassicheskie uravneniya Volterra I roda. Teoriya i chislennye metody, Nauka, Novosibirsk, 1999, 193 pp.

[9] R. M. Corless at al., “On the Lambert W function”, Advances Computational Maths., 5 (1996), 329–359 | DOI | MR | Zbl

[10] A. E. Dubinov, I. D. Dubinova, S. K. Saikov, W-funktsiya Lamberta i ee primenenie v matematicheskikh zadachakh fiziki, ucheb. posobie dlya vuzov, FGUP «RFYaTs-VNIIEF», Sarov, 2006, 160 pp.

[11] A. S. Apartsin, “O bilineinykh uravneniyakh Volterra I roda”, Optimizatsiya, upravlenie, intellekt, 2004, no. 8, 20–28

[12] A. S. Apartsin, “O skhodimosti chislennykh metodov resheniya bilineinogo uravneniya Volterra I roda”, Zhurn. vychisl. matematiki i mat. fiziki, 2007, no. 8, 1380–1388 | MR