Rate of Convergence of P-Iteration and S-Iteration for Continuous Functions on Closed Intervals

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 and S-iteration. We also compare the rate of convergence between P-iteration and S-iteration. Some numerical examples for comparing the rate of convergence of those two methods are also given.