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The solution to evolution equations has developed an independent theory within nonlinear analysis dealing with the existence and approximation of such solution(fixed point) of pseudocontractive operators and its variants.The object is to introduce a perturbed iteration method for proving the convergence of sequence of Lipschitzian pseudocontractive mapping using approximate fixed point technique.This iteration can be ued for nonlinear operators which are more general than Lipschitzian pseudocontractive operator and Bruck iteration fails for proving their convergence.Our results generalize the results of Chidume and Zegeye.