title: On generalization based on bi et Al. Iterative methods with eighth-order convergence for solving nonlinear equations.
abstract: The primary goal of this work is to provide a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per iteration with eighth-order convergence. Consequently, it satisfies Kung and Traub's conjecture relevant to construction optimal methods without memory. Moreover, some concrete methods of this class are shown and implemented numerically, showing their applicability and efficiency.
authors.affiliation: Department of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65188, Iran.
authors.forename: Taher
authors.initials: T
authors.lastname: Lotfi
authors.affiliation: Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain.
authors.forename: Alicia
authors.identifier: 0000-0002-7462-9173
authors.initials: A
authors.lastname: Cordero
authors.affiliation: Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain.
authors.forename: Juan R
authors.identifier: 0000-0002-9893-0761
authors.initials: JR
authors.lastname: Torregrosa
authors.affiliation: Department of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65188, Iran.
authors.forename: Morteza
authors.initials: M
authors.lastname: Amir Abadi
authors.affiliation: Department of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65188, Iran.
authors.forename: Maryam
authors.initials: M
authors.lastname: Mohammadi Zadeh
mesh_terms: D008962:Models, Theoretical