The generalized Newton--Kantorovich method for equations with nondifferentiable operators

TL;DR

This paper introduces a generalized Newton--Kantorovich method tailored for solving operator equations involving nondifferentiable operators in Banach spaces, with a convergence proof based on majorant scalar equations.

Contribution

It extends the Newton--Kantorovich method to nondifferentiable operators and provides a convergence theorem using majorant scalar equations.

Findings

Convergence of the method is established under certain conditions.

The approach broadens the applicability of Newton-type methods.

Theoretical analysis confirms the method's effectiveness for nondifferentiable operators.

Abstract

The article deals with the generalized Newton--Kantorovich method for solving operator equations with nondifferentiable operators in Banach spaces. The convergence theorem is proved by means of majorant scalar equations.