On the uniqueness of best approximation in Orlicz spaces

Ana Benavente; Juan Costa Ponce; Sergio Favier

doi:10.33205/cma.1883206

On the uniqueness of best approximation in Orlicz spaces

Abstract

We study uniqueness of best approximation in Orlicz spaces $L^{\Phi},$ for different types of not necessarily strictly convex functions $\Phi$ and for some finite dimensional approximation classes of functions, where Tchebycheff spaces, and more general approximation ones, are involved.

Keywords

Supporting Institution

Universidad Nacional de San Luis - CONICET

Project Number

PIP 694 CONICET

References

S. Acinas, S. Favier and R. Lorenzo: Extension of the Best Polynomial Operator in Generalized Orlicz Spaces, J. Approx. Theory, 310 (2025), Article ID: 106174.
S. Acinas, S. Favier: Multivalued Extended Best $\Phi$−Polynomial Approximation Operator, Numer. Funct. Anal. Optim., 37 (11) (2016), 1339–1353.
A. Benavente, S. Favier and F. Levis: Existence and characterization of best $\varphi$− approximations by linear subspaces, Adv. Pure Appl. Math., 8 (3) (2017), 209–217.
E. W. Cheney, D. E. Wulbert: The existence and unicity of best approximations, Math. Scand., 24 (1969), 113–140.
R. De Vore: One-sided approximation of functios, J. Approx. Theory, 1 (1968), 11–25.
R. V. Galkin: The uniqueness of the element of best mean approximation to a continuous function using splines with fixed nodes, Math. Notes, 15 (1974), 3–8.
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W. M.Kozlowski: On Modular Approximants in Sequential Convergence Spaces, J. Approx. Theory, 264 (2021), Article ID: 105535.

Details

Primary Language

English

Subjects

Real and Complex Functions (Incl. Several Variables)

Journal Section

Research Article

Authors

Ana Benavente This is me
0000-0003-2351-1746
Argentina

Juan Costa Ponce This is me
0009-0000-9112-5500
Argentina

Sergio Favier ^*
0000-0002-2395-7652
Argentina

Publication Date

June 16, 2026

Submission Date

February 15, 2026

Acceptance Date

June 7, 2026

Published in Issue

Year 2026 Volume: 9 Number: 2

DOI

https://doi.org/10.33205/cma.1883206

IZ

https://izlik.org/JA22SG63GC

Cite

RIS / Bibtex

APA

Benavente, A., Costa Ponce, J., & Favier, S. (2026). On the uniqueness of best approximation in Orlicz spaces. Constructive Mathematical Analysis, 9(2), 62-71. https://doi.org/10.33205/cma.1883206

AMA

1.Benavente A, Costa Ponce J, Favier S. On the uniqueness of best approximation in Orlicz spaces. CMA. 2026;9(2):62-71. doi:10.33205/cma.1883206

Chicago

Benavente, Ana, Juan Costa Ponce, and Sergio Favier. 2026. “On the Uniqueness of Best Approximation in Orlicz Spaces”. Constructive Mathematical Analysis 9 (2): 62-71. https://doi.org/10.33205/cma.1883206.

EndNote

Benavente A, Costa Ponce J, Favier S (June 1, 2026) On the uniqueness of best approximation in Orlicz spaces. Constructive Mathematical Analysis 9 2 62–71.

IEEE

[1]A. Benavente, J. Costa Ponce, and S. Favier, “On the uniqueness of best approximation in Orlicz spaces”, CMA, vol. 9, no. 2, pp. 62–71, June 2026, doi: 10.33205/cma.1883206.

ISNAD

Benavente, Ana - Costa Ponce, Juan - Favier, Sergio. “On the Uniqueness of Best Approximation in Orlicz Spaces”. Constructive Mathematical Analysis 9/2 (June 1, 2026): 62-71. https://doi.org/10.33205/cma.1883206.

JAMA

1.Benavente A, Costa Ponce J, Favier S. On the uniqueness of best approximation in Orlicz spaces. CMA. 2026;9:62–71.

MLA

Benavente, Ana, et al. “On the Uniqueness of Best Approximation in Orlicz Spaces”. Constructive Mathematical Analysis, vol. 9, no. 2, June 2026, pp. 62-71, doi:10.33205/cma.1883206.

Vancouver

1.Ana Benavente, Juan Costa Ponce, Sergio Favier. On the uniqueness of best approximation in Orlicz spaces. CMA. 2026 Jun. 1;9(2):62-71. doi:10.33205/cma.1883206