Argyros, I.K.George, S.Mohapatra, R.N.2026-02-052015Advances in Nonlinear Variational Inequalities, 2015, 18, 2, pp. 48-571092910Xhttps://idr.nitk.ac.in/handle/123456789/26350We present a local convergence analysis of a uniparametric Halley-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 [26]. Numerical examples are also provided in this study.Banach spaceFréchet-derivativeJarratt-type methodsLocal convergence