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Various problems of pure and applied sciences can be studied in the unified frame work of the nonlinear equations. In this paper, a new family of iterative methods for solving nonlinear equations is developed by using a new decomposition technique. The convergence of the proposed methods is proved. It is shown that the new family contains several well-known iterative methods as special case. For the implementation and performance of the new methods, a nonlinear equation arising in the population model and another one arising in the motion of a particle on inclined plane is solved. [ABSTRACT FROM AUTHOR]