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A new simple proof for an inequality of Chebyshev type. (English) Zbl 1131.26013

Summary: We give here a simple proof of the well-known integral version of the Chebyshev inequality. Using the same method, we give a lower bound in the case of increasing functions and then in the case of convex functions. We also establish a limit result which shows that the constant 1/12 is sharp, in the sense that it cannot be replaced by a smaller one.

MSC:

26D15 Inequalities for sums, series and integrals
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