Uniqueness of best approximation

Russian Mathematical Surveys, 2023
Existence and stability of $\varepsilon$-selections (selections of operators of near-best approximation) are studied. Results relating the existence of continuous $\varepsilon$-selections with other approximative and structural properties of approximating sets are given.
Alimov, Alexey R. +2 more
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On the uniqueness of best approximation in non-archimedian spaces

Periodica Mathematica Hungarica, 1991
\textit{A. F. Monna} [Indag. Math. 30, 484--496 (1968; Zbl 0172.39302)] has shown that 1. No subspace other than the trivial one of a non-Archimedean normed linear space (n.a. n.l.s.) $X$ over a non-Archimedean non-trivially valued field $K$, can be Chebyshev and 2.
Narang, T. D., Garg, S. K.
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Some remarks on strong uniqueness of best approximation

Approximation Theory and its Applications, 1990
In the paper we examine properties of strongly unique best approximation in terms of extremal functionals in an abstract normed linear space. Using some new or modified tools (e.g., the shadow of a set, strongly tangent sets, I-sets) we express criteria of strong uniqueness both in linear and nonlinear approximation.
J. Sudolski, A. P. Wójcik
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Characterizations of the strongly unique best approximations

Numerical Functional Analysis and Optimization, 1985
The purpose of this paper is two folded. First, we present some results on strongly Kolmogorov sets, some of which parallel those for Kolmogorov sets. Secondly, we give two conditions which are sufficient for an element of a strongly Kolmogorov set to be a strongly unique best approximation. Then these conditions are shown to be necessary if additional
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best approximation, chebyshev systems
applied mathematics
analysis

mathematics all
numerical analysis
approximation by polynomials

spline approximation
best approximation
uniqueness