Third order convergence theorem for a family of Newton like methods in Banach space

Abstract

In this paper, we propose a family of Newton-like methods in Banach space which includes some well known third-order methods as particular cases. We establish the Newton-Kantorovich type convergence theorem for a proposed family and get an error estimate.

Keywords

• nonlinear equations in Banach space
• third order Newton like methods
• recurrence relations
• error bounds
• convergence domain