Chebyshev method and convexity

摘要

From convexity we obtain new convergence theorems for the Chebyshev method applied to a nonlinear scalar equation f(x) = 0. Moreover, Kantorovich type conditions for the convergence of the Chebyshev method in the complex plane are given. Finally, a new type of assumptions are considered to prove the convergence of this method in Banach spaces.