Ball Convergence for two-parameter chebyshev-halley-like methods in banach space using hypotheses only on the first derivative

Abstract

We present a local convergence analysis of a sixth-order method for approximate a locally unique solution of an equation in the Banach space setting. The convergence of this methods is shown in Narang et al. (2016) under hypotheses up to the fourth Fréchet-derivative and the Lipschitz continuity of the third derivative, although only the first derivative appears in the method. In this study we expand the applicability of this method using only hypotheses on the first derivative of the function. Numerical examples are also presented in this study.