Generalised Newton ‒ Kantorovich method under the modified regular smoothness condition
Keywords:
generalised Newton – Kantorovich method, regular smoothness condition, non-linear operator equationAbstract
The article deals with the generalised Newton – Kantorovich method for solving non-linear operator equations of the form f(x) + g(x) = 0 in Banach spaces, where f is the operator satisfying the regular smoothness condition; g is the non-differentiable operator satisfying Lipschitz condition. The main convergence theorem is proved under the modified regular smoothness condition in which increments of the operator f derivative are majorised by the increments of a scalar function.
References
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Published
2026-01-04
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Real, Complex and Functional Analysis
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How to Cite
[1]
Tanyhina, A.N. 2026. Generalised Newton ‒ Kantorovich method under the modified regular smoothness condition. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Jan. 2026), 6–14.
