engleski

Variants of Chebyshev's inequality for two and for several n-tuples

Due to its wide applications in various fields of mathematics and other sciences, Chebyshev’s inequality is one of the most famous mathematical inequalities. Since its first proof in 1882 it has been studied extensively and numerous variants, generalizations, abstractions and applications appeared in literature. We present its variants of the Steffensen and Mercer type for two and for several n-tuples. We prove an identity for Chebyshev's functional of the Mercer type and use it to establish bounds for that functional and new refinements of the Chebyshev's inequality of the Mercer type. As an application we present some related double inequalities for sums.

Chebyshev’s inequality, n-tuples, Steffensen's conditions, Chebyshev's functional

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