Generalised Newton ‒ Kantorovich method under the modifjed regular smoothness condition

Abstract

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-difgerentiable operator satisfying Lipschitz condition. The main convergence theorem is proved under the modifjed regular smoothness condition in which increments of the operator f derivative are majorised by the increments of a scalar function.