A modification of the classical Kantorovich conditions for Newton's method

摘要

In the classical Kantorovich theorem on Newton's method it is assumed that the second Fréchet derivative of the involved operator satisfies the condition ||F″(x)||⩽K in an appropiate domain. In this paper we study a modification of this condition, assuming that ||F″(x)||⩽ω(||x||), where ω is a continuous and non-decreasing real function.