SavedAdd your journal

Journals / Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi / 2026 / Cilt: 35 Sayı: 3

Obtaining New Fixed Point Theorems Using Generalized Banach-Contraction Principle

Yunus Atalan(AKSARAY UNIVERSITY)0000-0002-5912-7087
Pages
34–45
Publication Date
2020-01-04
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)

In addition, it was shown that the new iterative algorithm has a better convergence speed when compared the other Jungck-type iterative algorithms in the current literature, and to support this result, numerical examples were given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a new three step iterative algorithm was introduced with the help of Jungck-contraction principle which is one of the remerkable generalizations of Banach-contraction principle.
📊
Key Findings & Data:Also, the convergence and stability results were obtained for the pair of nonself mappings which satisfy a certain contractive condition by using this iterative algorithm in any Banach space.
💡
Conclusion & Impact:In addition, it was shown that the new iterative algorithm has a better convergence speed when compared the other Jungck-type iterative algorithms in the current literature, and to support this result, numerical examples were given.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Jungck-contraction principle · New iterative algorithm · Convergence

Özet

In this study, a new three step iterative algorithm was introduced with the help of Jungck-contraction principle which is one of the remerkable generalizations of Banach-contraction principle. Also, the convergence and stability results were obtained for the pair of nonself mappings which satisfy a certain contractive condition by using this iterative algorithm in any Banach space. In addition, it was shown that the new iterative algorithm has a better convergence speed when compared the other Jungck-type iterative algorithms in the current literature, and to support this result, numerical examples were given.

🔖

Cite This Article

Atalan, Y. (2020). Obtaining New Fixed Point Theorems Using Generalized Banach-Contraction Principle. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, Cilt: 35 Sayı: 3, 34–45. https://ajindex.com/articles/1266922

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (22)

  1. Banach, S. 1922. Sur les operations dans les ensembles abstraites et leurs applications aux equations integrales. Fund. Math., 3, 133-181.
  2. Ciric, L. J. 1974. A generalization of Banach’s contraction principle. Proceedings of American Mathematical Society, 45, 267-273.
  3. Edelstein, M. 1961. An extension of Banach contraction principle. Proceedings of American Mathematical Society, 1, 7-10.
  4. Jungck, G. 1976. Commuting mappings and fixed points. American Mathematical Monthly, 83(4), 261-263.
  5. Presic, S. B. 1965. Sur Une Classe D’inequations Aux Differences Finite Et. Sur La Convergence De Certaines Suites. Publications de l'Institut Mathématique, 5(25), 75-78.
  6. Mann, W.R. 1953. Mean value methods in iteration. Proceedings of the American Mathematical Society, 4, 506–510.
  7. Ishikawa, S. 1974. Fixed points by a new iteration method. Proceedings of the American Mathematical Society, 44(1), 147–150.
  8. Noor, M.A. 2000. New approximation schemes for general variational inequalities. Journal of Mathematical Analysis and Applications, 251(1), 217–229.
  9. Atalan, Y. 2019. On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme. Konuralp Journal of Mathematics, 7(1), 97-106.
  10. Khan, A. R., Gürsoy, F., and Karakaya, V., 2016. Jungck-Khan iterative scheme and higher convergence rate. International Journal of Computer Mathematics, 93(12), 1029-2105.
  11. Singh, S.L., Bhatnagar, C. Mishra, S.N. 2005. Stability of Jungck-type iterative procedures. International Journal of Mathematics and Mathematical Sciences, 19, 3035–3043.
  12. Olatinwo, M.O. 2008. Some stability and strong convergence results for the Jungck-Ishikawa iteration process. Creative Mathematics and Informatics, 17, 33–42.
  13. Olatinwo, M.O. 2008. A generalization of some convergence results using a Jungck-Noor three-step iteration process in arbitrary Banach space. Polytechnica Posnaniensis, 40, 37–43.
  14. Chugh, R., Kumar, V. 2011. Strong Convergence and Stability results for Jungck-SP iterative scheme. International Journal of Computer Applications, 36(12), 40-46.
  15. Hussain, N., Kumar, V., Kutbi, M. A. 2013. On rate of convergence of Jungck-type iterative schemes, Abstract and Applied Analysis, 2013, 1-15.
  16. Khan, A. R., Kumar, V., Hussain, N. 2014. Analytical and numerical treatment of Jungck-type iterative schemes. Applied Mathematics and Computation, 231, 521-535.
  17. Phuengrattana W., Suantai, S. 2011. On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval. Journal of Computational and Applied Mathematics, 235(9), 3006–3014.
  18. Chugh, R., Kumar, V., Kumar, S. 2012. Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces. American Journal of Computational Mathematics, 2, 345-357.
  19. Chugh, R., Kumar, S. 2013. On the Stability and Strong Convergence for Jungck-Agarwal et al. Iteration Procedure International Journal of Computer Applications, 64(7), 39-44.
  20. Jungck, G., Hussain, N. 2007. Compatible maps and invariant approximations. J. Math. Anal. Appl., 325 (2), 1003-1012.
  21. Berinde, V. 2007. Iterative Approximation of Fixed Points, Springer, Berlin.
  22. Berinde, V. 2004. Picard iteration converges faster than the Mann iteration in the class of quasi-contractive operators. Fixed Point Theory Appl., 2, 97-105.