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Chebyshev type inequalities for pseudo-integrals

โœ Scribed by Hamzeh Agahi; Radko Mesiar; Yao Ouyang

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
470 KB
Volume
72
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

Chebyshev type inequalities for two classes of pseudo-integrals are shown. One of them concerning the pseudo-integrals based on a function reduces on the g-integral where pseudo-operations are defined by a monotone and continuous function g. Another one concerns the pseudo-integrals based on a semiring ([a, b], max, ), where is generated.

Moreover, a strengthened version of Chebyshev's inequality for pseudo-integrals is proved.

๐Ÿ“œ SIMILAR VOLUMES

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Denote by \(\eta_{i}=\cos (i \pi / n), i=0, \ldots, n\) the extreme points of the Chebyshev polynomial \(T_{n}(x)=\cos (n \operatorname{arc} \cos x)\). Let \(\pi_{n}\) be the set of real algebraic polynomials of degree not exceeding \(n\), and let \(B_{n}\) be the unit ball in the space \(\pi_{n}\)