Strict Protosuns in Asymmetric Spaces of Continuous Functions

Алимов, А. Р.

doi:10.1007/s00025-023-01876-9

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2023

2024

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Cited by 9 publications

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“…where f ∈ C(Q, R), and ψ + and ψ − are fixed positive continuous functions. Such norms were introduced in § 4 of [26]; solar and other approximative and geometric properties of sets in spaces with this norm, and also in more general spaces C 0;ψ+,ψ− , were studied in [2]. The asymmetric ball B(0, R) consists of all functions f lying between the functions Rψ + and −Rψ − , that is, satisfying…”

Section: )mentioning

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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Section: )mentioning

confidence: 99%