A note on a family of newton type iterative processes

Abstract

In this paper, we study the convergence of a family of iteration methods to solve nonlinear equations in the complex plane. Two analysis of convergence are provided. We give a Kan-torovich-type convergence theorem under mild differentiability conditions with error analysis.

Keywords:

• Nonlinear equations in complex plane
• second-order processes
• Newton method
• Newton-Kantorovich assumptions
• majorizing sequences

Classification A.M.S. 1991:

• 26A51
• 65H05