SOME FIXED POINT RESULTS FOR CONTINUOUS FUNCTIONS ON AN ARBITRARY INTERVALS

Year 2019, Volume: 37 Issue: 3, 755 - 767, 01.09.2020

Kadri Dogan Dogan Faik Gursoy Vatan Karakaya

Abstract

In this paper, we first give a necessary and sufficient condition for convergence of Picard-S iteration process to a fixed point of continuous functions on an arbitrary interval and prove equivalence of Picard-S and P iterative processes. We also compare the rate of convergence between Picard-S and some others iteration processes in the literature. Finally, some numerical examples for comparing the rate of convergence of those methods are also given.

Keywords

Rate of convergence, Picard-S iteration process, continuous function, closed interval

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