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

Maria Ines Gareis; Federico Dario Kovac; Fabian Eduardo Levis; Ludmila Zabala

doi:10.33205/cma.1886631

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

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 $\Gamma_{ w,q}$.

Keywords

Supporting Institution

Partially supported by Universidad Nacional de Río Cuarto, (Grant PPI 18/C614-2), Universidad Nacional de La Pampa, Facultad de Ingeniería (Grant Resol. Nro. 203/23), and CONICET (Grant PIP 112-202001-00694CO).

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Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Maria Ines Gareis
0009-0004-1681-8840
Argentina

Federico Dario Kovac ^*
0000-0002-3418-6312
Argentina

Fabian Eduardo Levis
0000-0002-5936-2239
Argentina

Ludmila Zabala
0009-0000-0691-1508
Argentina

Early Pub Date

August 11, 2026

Publication Date

-

Submission Date

February 12, 2026

Acceptance Date

August 6, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.33205/cma.1886631

IZ

https://izlik.org/JA47UY82PY

Cite

RIS / Bibtex

APA

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, Advanced Online Publication. https://doi.org/10.33205/cma.1886631

AMA

1.Gareis MI, Kovac FD, Levis FE, Zabala L. Quantitative estimates and near-best properties of extended best approximation in $\Gamma_{w,q}$ spaces for $0 < q \le 1$. CMA. 2026;(Advanced Online Publication). doi:10.33205/cma.1886631

Chicago

Gareis, Maria Ines, Federico Dario Kovac, Fabian Eduardo Levis, and Ludmila Zabala. 2026. “Quantitative Estimates and Near-Best Properties of Extended Best Approximation in $\Gamma_{w,q}$ Spaces for $0 < Q \le 1$”. Constructive Mathematical Analysis, no. Advanced Online Publication. https://doi.org/10.33205/cma.1886631.

EndNote

Gareis MI, Kovac FD, Levis FE, Zabala L (August 1, 2026) Quantitative estimates and near-best properties of extended best approximation in $\Gamma_{w,q}$ spaces for $0 < q \le 1$. Constructive Mathematical Analysis Advanced Online Publication

IEEE

[1]M. I. Gareis, F. D. Kovac, F. E. Levis, and L. Zabala, “Quantitative estimates and near-best properties of extended best approximation in $\Gamma_{w,q}$ spaces for $0 < q \le 1$”, CMA, no. Advanced Online Publication, Aug. 2026, doi: 10.33205/cma.1886631.

ISNAD

Gareis, Maria Ines - Kovac, Federico Dario - Levis, Fabian Eduardo - Zabala, Ludmila. “Quantitative Estimates and Near-Best Properties of Extended Best Approximation in $\Gamma_{w,q}$ Spaces for $0 < Q \le 1$”. Constructive Mathematical Analysis. Advanced Online Publication (August 1, 2026). https://doi.org/10.33205/cma.1886631.

JAMA

1.Gareis MI, Kovac FD, Levis FE, Zabala L. Quantitative estimates and near-best properties of extended best approximation in $\Gamma_{w,q}$ spaces for $0 < q \le 1$. CMA. 2026. doi:10.33205/cma.1886631.

MLA

Gareis, Maria Ines, et al. “Quantitative Estimates and Near-Best Properties of Extended Best Approximation in $\Gamma_{w,q}$ Spaces for $0 < Q \le 1$”. Constructive Mathematical Analysis, no. Advanced Online Publication, Aug. 2026, doi:10.33205/cma.1886631.

Vancouver

1.Maria Ines Gareis, Federico Dario Kovac, Fabian Eduardo Levis, Ludmila Zabala. Quantitative estimates and near-best properties of extended best approximation in $\Gamma_{w,q}$ spaces for $0 < q \le 1$. CMA. 2026 Aug. 1;(Advanced Online Publication). doi:10.33205/cma.1886631

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