Geometric constructions of iterative functions to solve nonlinear equations

By Sergio Amat, Sonia Busquier, J. Gutiérrez. 2003

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On Newton-type methods with cubic convergence (2005, methodology): “There exists an extension due to Potra and Pták called the “two-step method” [1] that may be rewritten as the iterative scheme xn+1 = xn − f (xn)+ f (xn − f (xn)/f ′(xn)) f ′(xn) (2)”
Some derivative free quadratic and cubic convergence iterative formulas for solving nonlinear equations (2010, background): “[2] considered a class of the generalized Steffensen iterations procedures for solving nonlinear equations on Banach space without any derivative.”
Review of some iterative root-finding methods from a dynamical point of view (2004, background): “As particular cases, this family of third{order iterative methods includes the following (see [ 3 ]).”
Some variants of Ostrowski's method with seventh-order convergence (2007, methodology): “A class of third-order methods, called Chebyshev–Halley methods [4,1], is given by”