The object of the present work is to give the new class ofthird- and fourth-order iterative methods for solving nonlinear equations. Our proposed third-order method includes methods of Weerakoon and Fernando (2000), Homeier (2005), and Chun and Kim (2010) as particular cases. The multivariate extension of some of thesemethods has been also deliberated. Finally, some numerical examplesare given to illustrate the performances of our proposed methods bycomparing them with some well existing third- and fourth-order methods. The efficiency of our proposed fourth-order method over somefourth-order methods is also confirmed by basins of attraction.
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