Local Convergence of Traub’s Method and Its Extensions

In this article, we examine the local convergence analysis of an extension Newton’s method in a Banach space setting. Traub introduced (also known as Arithmetic-Mean Method and Weerakoon Fernando method) with order three. All previous works either used higher-order Taylor series expansion or could not derive desired convergence. We studied Traub’s two its modifications obtained for these methods without using expansion. The radii convergence, basins attraction, comparison iterations similar iterative methods, approximate computational (ACOC), representation number are provided.