Suma, P.B.Erappa, S.M.George, S.2026-02-042022Results in Nonlinear Analysis, 2022, 5, 4, pp. 452-458https://doi.org/10.53006/rna.1138201https://idr.nitk.ac.in/handle/123456789/22246A sixth order Homeier-like method is introduced for approximating a solution of the non-linear equation in Banach space. Assumptions only on first and second derivatives are used to obtain a sixth order convergence. Our proof does not depend on Taylor series expansions as in the earlier studies for the similar methods. © 2022, Erdal Karapinar. All rights reserved.Banach spaceFrechet derivativeHomeier methodIterative methodLocal convergence