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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 40 Issue: 1

A Generalization of Jordan's Inequality and an Application ABSTRACT | FULL TEXT

Zh.-h. Huo
D.-w. Niu
J. Cao
f. Qi
Feng Qi
Pages
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Publication Date
2011-01-01
DOI
—
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AI Summary & Key Takeaways

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

As an application, Yang’s inequality is refine

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, a new generalization of Jordan’s inequality Xn k=1 µk θ t − x t k ≤ sin x x − sin θ θ ≤ Xn k=1 ωk θ t − x t k for t ≥ 2, n ∈ N and θ ∈ (0, π] is established, where the coefficients µk and ωk are defined by recursion formulas, and are the best possible.
📊
Key Findings & Data:In this article, a new generalization of Jordan’s inequality Xn k=1 µk θ t − x t k ≤ sin x x − sin θ θ ≤ Xn k=1 ωk θ t − x t k for t ≥ 2, n ∈ N and θ ∈ (0, π] is established, where the coefficients µk and ωk are defined by recursion formulas, and are the best possible.
💡
Conclusion & Impact:As an application, Yang’s inequality is refine
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:ds: Jordan’s inequali · Yang’s inequali

Abstract

In this article, a new generalization of Jordan’s inequality Xn k=1 µk θ t − x t k ≤ sin x x − sin θ θ ≤ Xn k=1 ωk θ t − x t k for t ≥ 2, n ∈ N and θ ∈ (0, π] is established, where the coefficients µk and ωk are defined by recursion formulas, and are the best possible. As an application, Yang’s inequality is refine

🔖

Cite This Article

Huo, Z., Niu, D., Cao, J., Qi, F., Qi, F. (2011). A Generalization of Jordan's Inequality and an Application ABSTRACT | FULL TEXT. Hacettepe Journal of Mathematics and Statistics, Volume: 40 Issue: 1. https://ajindex.com/articles/1403670

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