Some fixed point results for continuous functions on an arbitrary intervals
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KünyeDoğan, K., Gürsoy, F., & Karakaya, V. (2019). Some fixed point results for continuous functions on an arbitrary intervals. Sigma: Journal of Engineering & Natural Sciences/Mühendislik ve Fen Bilimleri Dergisi.37(3), 755-767.
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.