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2003•Journal of MathematicsRequires access

CHEBYSHEV'S INEQUALITY FOR A CLASS OF HOMOGENEOUS AND SYMMETRIC POLYNOMIALS

WE Jia

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Abstract

By means of majorized inequalities and mathematical induction, the well known Chebyshev's inequality is generalized to homogeneous and symmetric polynomials of degree m (e.g., Theorem and Lemma 7 of this paper). As an application, some inequalities involving symmetric mean and others are obtained. Our main purposes are to display some methods and techniques as well as to establish several new, useful and interesting analytic inequalities for mathematicl study (especially, for higher dimensional geometry).

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What this paper is about

By means of majorized inequalities and mathematical induction, the well known Chebyshev's inequality is generalized to homogeneous and symmetric polynomials of degree m (e.g., Theorem and Lemma 7 of this paper). As an application, some inequalities involving symmetric mean and others are obtained. Our main purposes are to display some methods and techniques as well as to establish several new, useful and interesting analytic inequalities for mathematicl study (especially, for higher dimensional geometry).

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Available abstract

By means of majorized inequalities and mathematical induction, the well known Chebyshev's inequality is generalized to homogeneous and symmetric polynomials of degree m (e.g., Theorem and Lemma 7 of this paper). As an application, some inequalities involving symmetric mean and others are obtained. Our main purposes are to display some methods and techniques as well as to establish several new, useful and interesting analytic inequalities for mathematicl study (especially, for higher dimensional geometry).

Key concepts: Mathematics, Lemma (botany), Homogeneous, Inequality, Chebyshev polynomials, Class (philosophy), Chebyshev filter, Multidimensional Chebyshev's inequality

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