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In this paper, we first give a necessary and sufficient condition for convergence of P-iteration to a fixed point of continuous functions on an arbitrary interval and prove equivalence of P-iteration, Noor and SP-iteration. We also compare the convergence speed of Noor, SP-iteration and P-iteration. It is proved that the P-iteration con verges faster than Noor and SP-iterations. Moreover, we also present numerical examples for the P-iteration to compare with the Noor and SP-iterations.

On the rate of convergence of Noor, SP and P-iterations for continuous functions on an arbitrary interval