Argyros, I.K.George, S.2026-02-052017Arab Journal of Mathematical Sciences, 2017, 23, 2, pp. 205-21413195166https://doi.org/10.1016/j.ajmsc.2016.10.002https://idr.nitk.ac.in/handle/123456789/25577We provide a local convergence analysis for a fifth convergence order method to find a solution of a nonlinear equation in a Banach space. In our paper the sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative. Previous works use conditions reaching up to the fourth Fréchet-derivative. This way, the applicability of these methods is extended under weaker conditions and less computational cost for the Lipschitz constants appearing in the convergence analysis. Numerical examples are also given in this paper. © 2016 The AuthorsBanach spaceFréchet-derivativeHigh convergence order methodLocal convergenceNonlinear equation