Argyros, I.K.George, S.2026-02-052016Asian-European Journal of Mathematics, 2016, 9, 1, pp. -17935571https://doi.org/10.1142/S1793557116500157https://idr.nitk.ac.in/handle/123456789/26053We present a local convergence analysis for the Jarratt-type method of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet-derivative. Hence, the applicability of these methods is expanded under weaker hypotheses and less computational cost for the constants involved in the convergence analysis. Numerical examples are also provided in this study. © World Scientific Publishing Company.Banach spaceFréchet-derivativeJarratt-type methodslocal convergence