The uniqueness of the best $L_1$-approximant of continuous Banach-valued functions under interpolatory constraints

We consider the best $L_1$-approximation with interpolatory constraints for continuous mapping of a metric compact set $Q$ into a Banach space $X$. The unicity set’s criterion is obtained. This result generalizes the result for real functions that was proved by A. Pinkus and H. Strauss.

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Publication Details

Journal
Researches in Mathematics
Published
2024-12-04
DOI
https://doi.org/10.15421/242427
Primary Topic
Mathematical Approximation and Integration
Type
article
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article

The uniqueness of the best $L_1$-approximant of continuous Banach-valued functions under interpolatory constraints

M.Ye. Tkachenko, V.M. Traktynska
Researches in Mathematics
Mathematical Approximation and Integration
article

The uniqueness of the best $L_1$-approximant of continuous Banach-valued functions under interpolatory constraints

M.Ye. Tkachenko, V.M. Traktynska
article en

Abstract

We consider the best $L_1$-approximation with interpolatory constraints for continuous mapping of a metric compact set $Q$ into a Banach space $X$. The unicity set’s criterion is obtained. This result generalizes the result for real functions that was proved by A. Pinkus and H. Strauss.

Researches in MathematicsVol. 32(2)
Oles Honchar Dnipro National University (UA)
Openalex Percentile: Top 62%
Mathematical Approximation and Integration
DOIOpen Access PDFOpenAlex
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The uniqueness of the best $L_1$-approximant of continuous Banach-valued functions under interpolatory constraints — M.Ye. Tkachenko, V.M. Traktynska · Researches in Mathematics (2024) | TGRS Research Map | TGRS