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Dergiler / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2019 / Cilt: 37 - Sayı: 3

SOME FIXED POINT RESULTS FOR CONTINUOUS FUNCTIONS ON AN ARBITRARY INTERVALS

Kadri Dogan DOGAN
Faik GURSOY
Vatan KARAKAYA
Sayfa
755–767
Yayın Tarihi
2020-09-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, some numerical examples for comparing the rate of convergence of those methods are also given.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri:We also compare the rate of convergence between Picard-S and some others iteration processes in the literature.
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Sonuç & Katkı:Finally, some numerical examples for comparing the rate of convergence of those methods are also given.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Rate of convergence · Picard-S iteration process · continuous function

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.

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Bu Makaleye Atıf Yap

DOGAN, K. D., GURSOY, F., KARAKAYA, V. (2020). SOME FIXED POINT RESULTS FOR CONTINUOUS FUNCTIONS ON AN ARBITRARY INTERVALS. Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt: 37 - Sayı: 3, 755–767. https://ajindex.com/articles/419147

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Kaynakça (16)

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  11. Karakaya, V., Dogan, K., Gursoy, F. and Erturk, M. (2013) Fixed point of a new three-step iteration algorithm under contractive-like operators over normed spaces, Abstract and Applied Analysis, vol. 2013, Article ID 560258, 9 pages, 2013
  12. Kadioglu, N., Yildirim, I. (2013) On the convergence of an iteration method for continuous mappings on an arbitrary interval, Fixed Point Theory Appl., 2013:124
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  14. Karahan I., Ozdemir, (2013) M. Fixed point problems of the Picard-Mann hybrid iterative process for continuous functions on an arbitrary interval, Fixed Point Theory and Applications 1 (2013): 244
  15. Gürsoy, F. Karakaya, V. (2014) A Picard-S hybrid type iteration method for solving a differential equation with retarded argument, arXiv preprint arXiv:1403.2546
  16. Sainuan, P. (2015) Rate of Convergence of P-Iteration and S-Iteration for Cont