SavedAdd your journal

Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2018 / Cilt: 18 - Sayı: 3

A Study On Faster Mann Iterative Method

Daha Hızlı Mann Sabit Nokta Yinelemesi Üzerine Bir Çalışma

Kadri DOĞAN
Pages
852–860
Publication Date
2022-10-12
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, it is shown that the Mann-type iterative process is faster than the classical Mann iterative process.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we introduce a Mann-type iterative method converges faster than Mann iterative method which is shown strong convergence to fixed point for almost contraction mappings in Banach spaces.
📊
Key Findings & Data:Also, we prove that the strong convergences of them are equal.
💡
Conclusion & Impact:Finally, it is shown that the Mann-type iterative process is faster than the classical Mann iterative process.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, we introduce a Mann-type iterative method converges faster than Mann iterative method which is shown strong convergence to fixed point for almost contraction mappings in Banach spaces. Also, we prove that the strong convergences of them are equal. Finally, it is shown that the Mann-type iterative process is faster than the classical Mann iterative process.

Özet

Bu çalışmada, Mann yineleme yönteminden daha hızlı olan Mann tipinde bir yinelemetanımlanmış ve bu yineleme yönteminin Banach uzaylarında hemen hemen büzülme dönüşümleriiçin sabit noktaya yakınsadığı gösterilmiştir. Ayrıca düzenlenmiş Mann yineleme yöntemininliteratürdeki diğer sabit nokta yineleme yöntemlerine yakınsaklık denklikleri ispatlanmıştır. Sonolarak, Mann tipindeki yineleme yönteminin, klasik Mann yineleme yönteminden daha hızlıolduğu gösterilmiştir.

🔖

Cite This Article

DOĞAN, K. (2022). A Study On Faster Mann Iterative Method. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 18 - Sayı: 3, 852–860. https://ajindex.com/articles/430017

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (10)

  1. Abbas, M. and Nazir, T., 2014. A new faster iteration process applied to constrained minimization and feasibility problems, Matematicki Vesnik 66 (2014) 223-234.
  2. Berinde, V., 2004. Picard iteration converges faster than Mann iteration for a class of quasi- contractive operators, Fixed Point Theory Appl. 2014:1. Fukhar-ud-din, H. and Berinde, V., 2016. Iterative methods for the class of quasi-contractive type operators and comparsion of their rate of convergence in convex metric spaces, Filomat 30, 223-230.
  3. Harder, A.M. and Hicks, T. L., 1988. Stability results for fixed point iteration procedures, Mathematica Japonica, 33, 693-706.
  4. Chugh, R., Malik, P. and Kumar, V., 2015. On a new faster implicit fixed point iterative scheme in convex metric spaces, J. Function Spaces, 2015, Article ID 905834. Gursoy, F. and Karakaya, V., 2014. A Picard-S hybrid type iteration method for solving a diferential equation with retarded argument, arXiv preprint arXiv:1403.2546 Karahan, I. and Ozdemir, M., 2013. A general iterative method for approximation of fixed points and their applications, Advances in Fixed Point Theory, 3, 510-526.
  5. 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, 2013, 9 pages. Dogan, K. and Karakaya, V., 2014. On the convergence and stability results for a new general iterative process, The Scienti_c World Journal, 2014, 8 pages. Sintunavarat, W. and Pitea, A., 2016. On a new iteration scheme for numerical reckoning fixedpoints of Berinde mappings with convergence analysis, J. Nonlinear Science Appl. 9, 2553-2562.
  6. Suantai, S., 2005. Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 311, 506-517.
  7. Reich, S. and Safrir, I., 1990. Nonexpansive iteration in hyperbolic spaces, Nonlinear. Anal. 15, 537-558
  8. Qihou, L., 2001. Iterative sequences for asymptotically quasi-nonexpansive mappings with error member, Journal of Mathematical Analysis and applications, 259(1), 18-24.
  9. Berinde, V., 2003. On the approximation of fixed points of weak contractive mappings, Carpathian J. Math, 19, 7 - 22. Berinde, V., 2007. Iterative Approximation of Fixed Points, Springer, Berlin, (2007).
  10. Phuengrattana, W. and Suantai, S., 2013. Comparison of the rate of convergence of various iterative methods for the class of weak contractions in Banach Spaces, Thai J. Math. 11,