Smoothness of subspace sections of the unit balls of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e38" altimg="si21.svg"><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e51" altimg="si22.svg"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>

Алимов, А. Р.; Tsar’kov, I. G.

doi:10.1016/j.jat.2021.105552

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Spaces With Asymmetric Distance and Their Generalizations1

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2023

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“…For other applications, also see [17]. In geometric approximation theory, asymmetric norms proved to be useful in many problems (see, for example, [4], [6], [27], [29], and [68]). Asymmetric distances also appear naturally in approximation theory (in particular, in problems of best one-sided approximations), serving as a 'bridge' between best approximation and best one-sided approximation.…”

Section: Spaces With Asymmetric Distance and Their Generalizationsmentioning

confidence: 99%

Existence, uniqueness, and stability of best and near-best approximations

Alimov,

Ryutin,

Tsar'kov

2023

Russian Math. Surveys

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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. Both abstract and concrete sets are considered - the latter include $n$-link piecewise linear functions, $n$-link $r$-polynomial functions and their generalizations, $k$-monotone functions, and generalized rational functions. Classical problems of the existence, uniqueness, and stability of best and near-best generalized rational approximations are considered. Bibliography: 70 titles.

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