Local convergence for a Chebyshev-type method free from second derivative in Banach spaces

In this paper, local convergence for a Chebyshev-type method free from second derivative is studied in Banach spaces. Previous studies prove convergence under conditions based on the third or higher derivative. However, we study the convergence under Lipschitz continuity conditions based on the first derivative. In contrast to the conditions used in previous studies, the conditions of our convergence are weaker. In this way, uniqueness of the solution and the radii of convergence balls also are analyzed. Also, Taylor expansion, which is often used in convergence analysis, is avoided. Thus the applicability of the method is extended. Two numerical examples are used to prove the criteria of convergence. Mathematics Subject Classification (2010). 99Z99; 00A00.