Geodesic
Generality of proof of theorems about iterative methods convergence
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 2 (2002), pp. 35-38 
V. M. Verzhbitsky. Generality of proof of theorems about iterative methods convergence. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 2 (2002), pp. 35-38. http://geodesic.mathdoc.fr/item/IIMI_2002_2_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Two theorems are presented, which allow to omit the end of proofs of convergence theorems about fast-convergent iterative methods of solving of nonlinear operator equations in Banach spaces.

[1] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1984, 742 pp. | MR | Zbl

[2] Ulm S. Yu., “Ob iteratsionnykh metodakh s posledovatelnoi approksimatsiei obratnogo operatora”, Izv. AN ESSR. Fiz., matem., 16:4 (1967), 403–411 | MR

[3] Verzhbitskii V. M., “O skhodimosti posledovatelnostei elementov banakhovykh prostranstv k nulyam nelineinykh operatorov”, Vestn. Perm. gos. tekh. un-ta, 2002 (to appear)

[4] Verzhbitskii V. M., Chislennye metody (lineinaya algebra i nelineinye uravneniya), Vyssh. shkola, M., 2000, 266 pp.

[5] Verzhbitskii V. M., Osnovy chislennykh metodov, Vyssh. shkola, M., 2002, 848 pp.