On the convergence of inexact Newton-like methods under mild differentiability conditions

Abstract

In the present paper, we have introduced an inexact Newton-like algorithm and discussed its semilocal convergence analysis under average Lipschitz condition as well as γ-Lipschitz condition for solving generalized operator equations containing non differentiable operators in Banach spaces. Our results extend and improve some well established results in the context of differentiability of involved operators. As special cases of our results, we re-obtain some well established results for the Newton method and inexact Newton method. We apply our result to solve Fredholm integral equations.