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CHEBYSHEV INEQUALITY ANDBOUNDS OF CHEBYSHEV FUNCTIONAL

Pangeran Bottor Halomoan Pakpahan

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Abstract

Chebyshev Inequality compares the integral mean of the product of two functions that have the same monotony with the product of the integral means. In this final project we present the proof of Chebyshev Inequality and its generalization in a determinant form. In addtion, we discuss Chebyshev Functional that is used to approximate the integral mean of the product of two functions by the product of the integral means. Furthermore, bounds of Chebyshev Functional for functions of bounded variation involving Riemann-Stieltjes integral are discussed. Keywords: Chebyshev Inequality, Chebyshev Functional, function of bounded variation, Riemann-Stieltjes integral.

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What this paper is about

Chebyshev Inequality compares the integral mean of the product of two functions that have the same monotony with the product of the integral means. In this final project we present the proof of Chebyshev Inequality and its generalization in a determinant form. In addtion, we discuss Chebyshev Functional that is used to approximate the integral mean of the product of two functions by the product of the integral means. Furthermore, bounds of Chebyshev Functional for functions of bounded variation involving Riemann-Stieltjes integral are discussed. Keywords: Chebyshev Inequality, Chebyshev Functional, function of bounded variation, Riemann-Stieltjes integral.

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Available abstract

Chebyshev Inequality compares the integral mean of the product of two functions that have the same monotony with the product of the integral means. In this final project we present the proof of Chebyshev Inequality and its generalization in a determinant form. In addtion, we discuss Chebyshev Functional that is used to approximate the integral mean of the product of two functions by the product of the integral means. Furthermore, bounds of Chebyshev Functional for functions of bounded variation involving Riemann-Stieltjes integral are discussed. Keywords: Chebyshev Inequality, Chebyshev Functional, function of bounded variation, Riemann-Stieltjes integral.

Key concepts: Multidimensional Chebyshev's inequality, Mathematics, Chebyshev filter, Riemann–Stieltjes integral, Chebyshev polynomials, Bounded variation, Generalization, Chebyshev equation

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