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<正> 0 IntroductionWe seek methods for obtaining a simple zero x~* of the function f(x).The aim isto develop iterative processes of order p,in the error equationε_(k+1)=Kε_k~p+O(ε_k~(p+1)),as ε_k→0for ε_k=x_k-x~* and Ka function only of the derivativ