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Journals / Constructive Mathematical Analysis / 2026 / Volume: 9 Issue: 3

Quantitative estimates and near-best properties of extended best approximation in $\Gamma_{w,q}$ spaces for \(0 < q \le 1\)

Maria Ines Gareis(Universidad Nacional de La Pampa)0009-0004-1681-8840
Federico Dario Kovac(Universidad Nacional de La Pampa)0000-0002-3418-6312
Fabian Eduardo Levis(Universidad Nacional de Rio Cuarto)0000-0002-5936-2239
Ludmila Zabala(Universidad Nacional de Rio Cuarto)0009-0000-0691-1508
Pages
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Publication Date
2026-09-15
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AI Summary & Key Takeaways

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

As a consequence, we show that extended best approximations in \(\Gamma_{ w,1}\) are near-best approximations in \(\Gamma_{ w,q}\).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This article investigates the extended best polynomial approximation operator, defined on the space of measurable functions, within the setting of Lorentz Gamma spaces \(\Gamma_{ w,q}\) for \(0 < q \le 1\).
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Key Findings & Data:We derive quantitative estimates for extended best approximations and the outer operator quasi-norm.
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Conclusion & Impact:As a consequence, we show that extended best approximations in \(\Gamma_{ w,1}\) are near-best approximations in \(\Gamma_{ w,q}\).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Lorentz Gamma spaces · inequalities · approximation by polynomials

Abstract

This article investigates the extended best polynomial approximation operator, defined on the space of measurable functions, within the setting of Lorentz Gamma spaces \(\Gamma_{ w,q}\) for \(0 < q \le 1\). We derive quantitative estimates for extended best approximations and the outer operator quasi-norm. As a consequence, we show that extended best approximations in \(\Gamma_{ w,1}\) are near-best approximations in \(\Gamma_{ w,q}\).

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Cite This Article

Gareis, M. I., Kovac, F. D., Levis, F. E., Zabala, L. (2026). Quantitative estimates and near-best properties of extended best approximation in $\Gamma_{w,q}$ spaces for \(0 < q \le 1\). Constructive Mathematical Analysis, Volume: 9 Issue: 3. https://doi.org/10.33205/cma.1886631

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