On the convergence of S-iteration process of Inexact Newton-Kantorovich like methods

Abstract

A plethora of Newton-like methods are used for solving one or more time
Fr\'echet differentiable operator equations in Banach spaces. This
article'smain tactic is to use the S-iterative approach to accelerate
inexact Newton method's convergence while avoiding the differentiability condition. In the present article, we have introduced a new S-iteration process of inexact Newton-Kantorovich like method to approximate the solution of non differentiable operator equations in Banach space settings and examined its semilocal convergence analysis with modest assumptions and weak Lipschitz conditions. The main result improves and extends some published results in the context of speed of convergence and differentiability of involved operator and the special cases of our main result are some well-known results. Finally, we apply our results to solve the system of linear equations and Fredholm integral equations, where some pre established results cannot apply.