Abstract

We study third-order Newton-type methods free of bilinear operators for solving nonlinear equations in Banach spaces. Our convergence conditions are weaker than the conditions used in earlier studies. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.

Keywords: Newton's method; bilinear operator; radius of convergence; local convergence.

MSC: 49M15, 74G20, 41A25

Pages:  1$-$11     

Volume  70 ,  Issue  1 ,  2018