Existence, uniqueness, and stability of best and near-best approximationsстатья
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Дата последнего поиска статьи во внешних источниках: 15 февраля 2024 г.
Аннотация:Existence and stability of $\varepsilon$-selections (selections of the operators of near-best approximation) are studied.Results relating the existence of continuous $\varepsilon$-selections with other approximative andstructural properties of approximating sets are given.Both abstract and concrete sets are considered\,---\,among the latter we mention:$n$-link piecewise linear functions,$n$-link $r$-polynomial functions and their generalizations,$k$-monotone functions, and generalized rational functions.Classical problems of existence, uniqueness, and stability of best and near-bestgeneralized rational approximation are considered.