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Journals / İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi / 2016 / Cilt: 15 Sayı: 30

Convergence Analysis For a New Faster Iteration Method

Daha Hızlı Yeni Bir İterasyon Metodu İçin Yakınsaklık Analizi

Vatan Karakaya(Yıldız Technical University)
Yunus Atalan(Yıldız Technical University)
Kadri Doğan(ARTVIN CORUH UNIVERSITY)
Nour El Houda Bouzara(Yıldız Technical University)
Pages
35–53
Publication Date
2016-12-31
DOI
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AI Summary & Key Takeaways

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

Finally, we prove a data dependence result for almost contraction mappings by using the new iteration method

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce a new iteration method and show that this iteration method can be used to approximate fixed point of almost contraction mappings.
📊
Key Findings & Data:Furthermore, we prove that the new iteration method is equivalent to both Mann iteration method and Picard-Mann hybrid iteration method and also converges faster than Picard-Mann hybrid iteration method for the class of almost contraction mappings.
💡
Conclusion & Impact:Finally, we prove a data dependence result for almost contraction mappings by using the new iteration method
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we introduce a new iteration method and show that this iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that the new iteration method is equivalent to both Mann iteration method and Picard-Mann hybrid iteration method and also converges faster than Picard-Mann hybrid iteration method for the class of almost contraction mappings. In addition to these we give a table and graphics for support this result. Finally, we prove a data dependence result for almost contraction mappings by using the new iteration method

Özet

Bu makelde yeni bir iterasyon yöntemini tanımladık ve bu iterasyon yönteminin hemen hemen büzülme dönüşümlerinin sabit noktasına yaklaşımı için kullanılabilir olduğunu gösterdik. Ayrıca, yeni iterasyon yönteminin hem Mann iterasyon yöntemi hem de Picard-Mann hibrid iterasyon yöntemine denk olduğunu ve hemen hemen büzülme dönüşümleri sınıfı için Picard-Mann hibrid iterasyon yönteminden daha hızlı yakınsadığını kanıtladık. Bunlara ek olarak, bu sonucu destekleyen bir tablo ve grafik de verdik. Son olarak, yeni iterasyon yöntemini kullanarak hemen hemen büzülme dönüşümleri için bir veri bağlılığı sonucunu kanıtladık.

Keywords
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Cite This Article

Karakaya, V., Atalan, Y., Doğan, K., Bouzara, N. E. H. (2016). Convergence Analysis For a New Faster Iteration Method. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi, Cilt: 15 Sayı: 30, 35–53. https://ajindex.com/articles/1171194

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