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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We estimate the degree of comonotone polynomial approximation of continuous functions f , on [−1,1], that change monotonicity s ≥ 1 times in the interval, when the degree of unconstrained polynomial approximation En(f ) ≤ n−α , n ≥ 1. We ask whether the degree of comonotone approximation is necessarily ≤ c(α, s)n−α , n ≥ 1, and if not, what can be said. It turns out that for each s ≥ 1, there i...
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This paper focuses on the study of decision making under risk. We, first, recall some model-free definitions of risk aversion and increase in risk. We propose a new form of behavior under risk that we call anti-monotone risk aversion (hereafter referred to as ARA) related to the concept of anti-comonotony a concept investigated in Abouda, Aouani and Chateauneuf (2008). Note that many research h...
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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: Proceedings of the American Mathematical Society
سال: 1974
ISSN: 0002-9939
DOI: 10.2307/2039514