ON THE RATE OF CONVERGENCE OF PICARD AND PICARD-MANN HYBRID ITERATIONS FOR CONTINUOUS FUNCTIONS ON AN ARBITRARY INTERVAL

Abstract

In this paper, we compare the rate of convergence of Picard and Picard-Mann hybrid iterations under the same computational cost. A numerical example is provided which supports the theoretical result. Finally, we use the example provided by Chidumeand Mutangadura [2] to show that the Picard-Mann hybrid iteration fails to converge for a Lipschitz pseudocontractive map with a unique fixed point.