Mortici, Cristinel A new simple proof for an inequality of Chebyshev type. (English) Zbl 1131.26013 An. Științ. Univ. “Ovidius” Constanța, Ser. Mat. 13, No. 2, 39-44 (2005). 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 Keywords:Chebyshev inequality; Riemann integrals PDFBibTeX XMLCite \textit{C. Mortici}, An. Științ. Univ. ``Ovidius'' Constanța, Ser. Mat. 13, No. 2, 39--44 (2005; Zbl 1131.26013) Full Text: EuDML