A counterexample in comonotone approximation in $L^p$ space
نویسندگان
چکیده
منابع مشابه
Nearly Comonotone Approximation
We discuss the degree of approximation by polynomials of a function f that is piecewise monotone in ?1; 1]. We would like to approximate f by polynomials which are comonotone with it. We show that by relaxing the requirement for comonotonicity in small neighborhoods of the points where changes in monotonicity occur and near the endpoints, we can achieve a higher degree of approximation. We show...
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When we approximate a continuous function f which changes its monotonicity nitely many, say s times, in ?1; 1], we wish sometimes that the approximating polynomials follow these changes in monotonicity. However, it is well known that this requirement restricts very much the degree of approximation that the polynomials can achieve, namely, only the rate of ! 2 (f; 1=n) and even this not with a c...
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Let En(f) denote the degree of approximation of f ∈ C[−1, 1], by algebraic polynomials of degree < n, and assume that we know that for some α > 0 and N ≥ 2, nEn(f) ≤ 1, n ≥ N. Suppose that f changes its monotonicity s ≥ 1 times in [−1, 1]. We are interested in what may be said about its degree of approximation by polynomials of degree < n that are comonotone with f . In particular, if f changes...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1993
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-64-2-265-274