Title | A generalization of the Newton—Kantorovich theorem in a banach space |
Publication Type | Journal Article |
Year of Publication | 2018 |
Authors | Chuiko, SM |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2018.06.022 |
Issue | 6 |
Section | Mathematics |
Pagination | 22-31 |
Date Published | 6/2018 |
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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