Geodesic
The convergence of successive approximations method for $p$-adic matrices
Trudy Instituta matematiki, Tome 25 (2017) no. 1, pp. 27-38.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article deals with the necessary and sufficient conditions for the convergence of successive approximations of approximate solving linear systems with $p$-adic coefficients. Also, some modifications of these conditions for linear equations in Banach spaces over the field of $p$-adic numbers are presented. 
@article{TIMB_2017_25_1_a2,
     author = {P. P. Zabreiko},
     title = {The convergence of successive approximations method for $p$-adic matrices},
     journal = {Trudy Instituta matematiki},
     pages = {27--38},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2017_25_1_a2/}
}
TY  - JOUR
AU  - P. P. Zabreiko
TI  - The convergence of successive approximations method for $p$-adic matrices
JO  - Trudy Instituta matematiki
PY  - 2017
SP  - 27
EP  - 38
VL  - 25
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2017_25_1_a2/
LA  - ru
ID  - TIMB_2017_25_1_a2
ER  - 
%0 Journal Article
%A P. P. Zabreiko
%T The convergence of successive approximations method for $p$-adic matrices
%J Trudy Instituta matematiki
%D 2017
%P 27-38
%V 25
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2017_25_1_a2/
%G ru
%F TIMB_2017_25_1_a2
P. P. Zabreiko. The convergence of successive approximations method for $p$-adic matrices. Trudy Instituta matematiki, Tome 25 (2017) no. 1, pp. 27-38. http://geodesic.mathdoc.fr/item/TIMB_2017_25_1_a2/

[1] Danford N., Shvarts D. T., Lineinye operatory. Obschaya teoriya, Izd-vo IL, M., 1962

[2] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nevskii dialekt, SPb, 2004

[3] Krasnoselskii M. A., Vainikko G. M., Zabreiko P. P., Rutitskii Ya. B., Stetsenko V. Ya., Priblizhennye metody resheniya operatornykh uravnenii, Nauka, M., 1969

[4] Khille E., Fillips R., Funktsionalnyi analiz i polugruppy, Izd-vo IL, M., 1962

[5] Zabreiko P. P., Mikhailov A. V., “Ob obobschenii teoremy M. A. Krasnoselskogo na nesamosopryazhennye operatory”, Dokl. NAN Belarusi, 58:2 (2014), 16–24

[6] Katok S. B., $p$-Adicheskii analiz v sravnenii s veschestvennym, MTsNMO, M., 2004

[7] Koblits N., $p$-Adicheskie chisla, $p$-adicheskii analiz i dzeta-funktsii, Mir, M., 1982

[8] Mahler K., $p$-Adic numbers and their functions, Cambridge University Press, Cambridge, 1881 | MR

[9] Radyno A. Ya., Radyno Ya. V., Elementarnyya ŭvodziny ŭ $p$-adychny analiz, BDPU, Minsk, 2006

[10] Radyno Ya. V., Radyno A. Ya., Radyno E. M., Pachatki nearkhimedova analizu, BDU, Minsk, 2010

[11] van Rooij A., Non-archimedean functional analysis, Pure and Applied Math., 51, Marcel Dekker, New York, 1978 | MR

[12] Schikhof W. H., Introduction to $p$-adic numbers and their functions, Cambridge University Press, Cambridge, 1973 | MR

[13] Schikhof W. H., Ultrametric calculus. An introduction to $p$-adic analysis, Cambridge University Press, Cambridge, 1984 | MR

[14] Schikhof W. H., A crash course in $p$-adic analysis, Springer Verlag, 2002

[15] Schneider P., Nonarchimedean Functional Analysis, Springer Monographs in Mathematics, Springer Verlag, 2002 | DOI | MR