A generalization of the Newton—Kantorovich theorem in a banach space

1Chuiko, SM
1Donbass State Pedagogical University, Slovyansk
Dopov. Nac. akad. nauk Ukr. 2018, 6:22-31
https://doi.org/10.15407/dopovidi2018.06.022
Section: Mathematics
Language: Ukrainian
Abstract: 

We present a modification of the Newton—Kantorovich method for nonlinear operator equations in a Banach space. We prove, under certain conditions, that this modified Newton—Kantorovich method has quadratic convergence. The modified Newton—Kantorovich method is used to solve some nonlinear integral and integral- differential equations.

Keywords: Banach space, modification of the Newton—Kantorovich method, nonlinear operator equations, quadratic convergence
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