Fixed point problems of the Picard-Mann hybrid iterative process for continuous functions on an arbitrary interval

Abstract

In this paper, we consider the iteration method called 'Picard-Mann hybrid iterative process' for finding a fixed point of continuous functions on an arbitrary interval. We give a necessary and sufficient condition for convergence of this iteration for continuous functions on an arbitrary interval. Also, we compare the rate of convergence of the Picard-Mann hybrid iteration with the other iterations and prove that it is better than the others under the same computational cost. Moreover, we present numerical examples. ©2013 Karahan and Ozdemir; licensee Springer.