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On the convergence of Ulm’s method for equations with regularly smooth operators. (Russian. English summary) Zbl 06963940
Summary: The article deals with Ulm’s method for solving nonlinear operator equations in Banach spaces under the regular smoothness assumption of the operator involved. The convergence theorem is proved and the error bounds for the method are obtained.
MSC:
47J Equations and inequalities involving nonlinear operators
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Full Text: MNR
References:
[1] [1] Ulm S., “Ob iteratsionnykh metodakh s posledovatelnoi approksimatsiei obratnogo operatora”, Izv. AN Estonskoi SSR, 16:4 (1967), 403–411
[2] [2] Galperin A., Waksman Z., “Ulm’s method under regular smoothness”, Numer. Funct. Anal. and Optimiz., 19:3–4 (1998), 285–307 · Zbl 0909.65032
[3] [3] Galperin A., Waksman Z., “Regular smoothness and Newton’s method”, Numer. Funct. Anal. and Optimiz., 15:7–8 (1994), 813–858 · Zbl 0814.65054
[4] [4] Zabreiko P. P., Tanygina A. N., “Uslovie regulyarnoi gladkosti i metod Nyutona–Kantorovicha”, Tr. In-ta matematiki NAN Belarusi, 19:1 (2011), 52–61 · Zbl 1261.65059
[5] [5] Galperin A., Waksman Z., “Newton’s method under a weak smoothness assumption”, J. Comp. Appl. Math., 35 (1991), 207–215 · Zbl 0755.65057
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