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

TitleA generalization of the Newton—Kantorovich theorem in a banach space
Publication TypeJournal Article
Year of Publication2018
AuthorsChuiko, SM
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
Date Published6/2018

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.

KeywordsBanach space, modification of the Newton—Kantorovich method, nonlinear operator equations, quadratic convergence
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