SOME FIXED POINT RESULTS FOR CONTINUOUS FUNCTIONS ON AN ARBITRARY INTERVALS


Dogan K., Gursoy F., KARAKAYA V.

SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, cilt.37, ss.755-767, 2019 (ESCI İndekslerine Giren Dergi)

  • Cilt numarası: 37 Konu: 3
  • Basım Tarihi: 2019
  • Dergi Adı: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
  • Sayfa Sayısı: ss.755-767

Özet

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.