A new iterative method of asymptotic order 1+√2 for the computation of fixed points

Abstract

We introduce a new iterative method of asymptotic order 1+√2 for approximating fixed points of non-linear equations in a Banach space as well as in a partially topological space. The method requires less computational cost than others in the literature and uses only divided differences of order 1.

Keywords:

• Banach space
• POTL space
• Contraction mapping theorem
• Local Convergence
• Semilocal Convergence
• Monotone convergence
• Newton-like methods
• Divided differences