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Some complements to the Jensen and Chebyshev inequalities and a problem of W. Walter

Author(s): S. M. Malamud
Journal: Proc. Amer. Math. Soc. 129 (2001), 2671-2678.
MSC (1991): Primary 26D15
Posted: February 15, 2001
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Abstract: Motivated by an integral inequality conjectured by W. Walter, we prove some general integral inequalities on finite intervals of the real line. In addition to supplying new proofs of Walter's conjecture, the general inequalities furnish a reverse Jensen inequality under appropriate conditions and provide generalizations of Chebyshev's integral inequality.

References:

1.: P.J. Bushell and W. Okrasínski, Nonlinear Volterra Integral Equations with Convolution Kernel, J. London Math. Soc. (2)41 (1990), 503-510. MR 91g:45001
2.: Yu. V. Egorov, On the best constant in a Poincaré-Sobolev inequality, Operator Theory: Advances and Applications (to appear).
3.: W. Walter, Problem: An integral inequality by Bushell and Okrasínski, Intern. series of Numerical Mathematics Vol. 103 (1992).
4.: W. Walter and V. Weckesser, An integral inequality of convolution type, Aequationes Mathematicae 46 (1993), 369-376. MR 94e:26030


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