George, S.Argyros, I.K.Senapati, K.Kanagaraj, K.2026-02-042022Journal of Analysis, 2022, 30, 4, pp. 1497-15089713611https://doi.org/10.1007/s41478-022-00415-zhttps://idr.nitk.ac.in/handle/123456789/22303In this paper we consider two three-step iterative methods with common first two steps. The convergence order five and six, respectively of these methods are proved using assumptions on the first derivative of the operator involved. We also provide dynamics of these methods © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.Banach spaceDynamics of iterative methodFréchet derivativeIterative methodOrder of convergence