Some Fixed Point Results for Continuous Functions on an Arbitrary Intervals
1Artvin Coruh University, Department of Computer Engineering, ARTVIN
2Department of Mathematics, Adiyaman University, ADIYAMAN
3Yildiz Technical University, Department of Mathematical Engineering, ISTANBUL
2Department of Mathematics, Adiyaman University, ADIYAMAN
3Yildiz Technical University, Department of Mathematical Engineering, ISTANBUL
Sigma J Eng Nat Sci 2019; 37(3): 755-767
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.
