Local convergence analysis for Chebyshev’s method

摘要

In this work, we are working to present a local convergence analysis for Chebyshev’s method by using majorizing sequence. The given method is a third order iterative process, used in order to approximate a zero of an nonlinear operator equation in a Banach space. Here we are using a new type of majorant conditions to prove the convergence. We will also try to establish relations between this majorant conditions with results of based on Kantorovich-type and Smale-type assumptions.