منابع مشابه
SOME ESTIMATES FOR CONVEX POLYNOMIAL APPROXIMATION IN Lp
We prove a direct theorem for convex polynomial L p-approximation, 0 < p < 1, in terms of the classical modulus of smoothness ! 3 (f; t) p. This theorem may be regarded as an extension to L p of the well-known pointwise estimates of the Timan type and their variants of R. DeVore, Y. K. Hu and D. Leviatan for convex approximation in L p. It leads to a characterization of convex functions in Lips...
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We prove that a convex function f 6 L p [ -1 , 1], 0 < p < cx~, can be approximated by convex polynomials with an error not exceeding Cw~ (f, 1/n)p where w~(f, .) is the Ditzian-Totik modulus of smoothness of order three of f . We are thus filling the gap between previously known estimates involving og~(f, I/n)p, and the impossibility of having such estimates involving ~o4. We also give similar...
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In this paper, the problem of approximating a function defined on a finite subset of the real line by a family of generalized rational functions whose numerator and denominator spaces satisfy the Haar conditions on some closed interval [a, b] containing the finite set is considered. The pointwise closure of the family restricted to the finite set is explicitly determined. The representation obt...
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Much of the recent literature on risk measures is concerned with essentially bounded risks in L∞. In this paper we investigate in detail continuity and representation properties of convex risk measures on L spaces. This frame for risks is natural from the point of view of applications since risks are typically modelled by unbounded random variables. The various continuity properties of risk mea...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1988
ISSN: 0021-9045
DOI: 10.1016/0021-9045(88)90105-0