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In this paper we consider a geometric construction of iteration functions of order three to develop cubically convergent iterative methods for solving nonlinear equations. This construction can be applied to any iteration function of order two to develop an iteration function of order three. Some examples are given of deriving several third-order iteration methods, and several numerical results follow to illustrate the performance of the derived methods.doi:10.1016/j.camwa.2007.01.007 fatcat:t5cwssbkkzeuzcuqmysajy23ra