The convergence theorem for fourth-order super-Halley method in weaker conditions

Abstract

Abstract In this paper, we establish the Newton-Kantorovich convergence theorem of a fourth-order super-Halley method under weaker conditions in Banach space, which is used to solve the nonlinear equations. Finally, some examples are provided to show the application of our theorem.

Keywords

• nonlinear equations in Banach spaces
• super-Halley method
• semilocal convergence
• Newton-Kantorovich theorem
• weaker conditions