ON THE SOLUTION OF NONLINEAR EQUATIONS CONTAINING A NON-DIFFERENTIABLE TERM

ON THE SOLUTION OF NONLINEAR EQUATIONS CONTAINING A NON-DIFFERENTIABLE TERM

We approximate a locally unique solution of a nonlinear operator equation containing a non-differentiable operator in a Banach space setting using Newton's method. Sufficient conditions for the semilocal convergence of Newton's method in this case have been given by several authors using mainly increasing sequences [1]-[6]. Here, we use center as well as Lipschitz conditions and decreasing majorizing sequences to obtain new sufficient convergence conditions weaker than before in many interesting cases. Numerical examples where our results apply to solve equations but earlier ones cannot [2], [5], [6] are also provided in this study.