SOME FIXED POINT RESULTS FOR CONTINUOUS FUNCTIONS ON AN ARBITRARY INTERVALS
SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, vol.37, no.3, pp.755-767, 2019 (ESCI)
- Publication Type: Article / Article
- Volume: 37 Issue: 3
- Publication Date: 2019
- Journal Name: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
- Journal Indexes: Emerging Sources Citation Index (ESCI), Academic Search Premier, Directory of Open Access Journals
- Page Numbers: pp.755-767
- Yıldız Technical University Affiliated: Yes
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.