Generalised Newton ‒ Kantorovich method under the modified regular smoothness condition - Tanyhina, Anastasija N. (Journal of the Belarusian State University. Mathematics and Informatics, 2026)
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.
Keywords: generalised Newton – Kantorovich method; regular smoothness condition; non-linear operator equation