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Journals / Results in Nonlinear Analysis / 2026 / 2022 - Cilt 5, Sayı 4

On the convergence of the sixth order Homeier like method in Banach spaces

Suma P B(manipal institute of technology)
M. E. Shobha(Manipal Institute of Technology)
Santhosh George(National Institute of Technology Karnataka)
Pages
452–458
Publication Date
2022-12-30
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AI Summary & Key Takeaways

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

Our proof does not depend on Taylor series expansions as in the earlier studies for the similar methods.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A sixth order Homeier-like method is introduced for approximating a solution of the non-linear equation in Banach space.
📊
Key Findings & Data:Assumptions only on first and second derivatives are used to obtain a sixth order convergence.
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Conclusion & Impact:Our proof does not depend on Taylor series expansions as in the earlier studies for the similar methods.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Frechet derivative · Frechet derivative · Homeier method

Abstract

A sixth order Homeier-like method is introduced for approximating a solution of the non-linear equation in Banach space. Assumptions only on first and second derivatives are used to obtain a sixth order convergence. Our proof does not depend on Taylor series expansions as in the earlier studies for the similar methods.

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Cite This Article

B, S. P., Shobha, M. E., George, S. (2022). On the convergence of the sixth order Homeier like method in Banach spaces. Results in Nonlinear Analysis, 2022 - Cilt 5, Sayı 4, 452–458. https://doi.org/10.53006/rna.1138201

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