LOCAL CONVERGENCE FOR A FAMILY OF CUBICALLY CONVERGENT METHODS IN BANACH SPACE

Abstract

We present a local convergence analysis for a family of cubically convergent methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. We only use hypotheses on the first Fr ́echet-derivative. The local convergence analysis in [6, 15] used hypotheses up to the second Fr ́echet derivative. Hence, the application of the methods is extended under less computational cost. This work also provides computable convergence ball and computable error bounds. Numerical examples are also provided in this study.