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

Author: S. M. Malamud
Journal: Proc. Amer. Math. Soc. 129 (2001), 2671-2678
MSC (1991): Primary 26D15
Published electronically: February 15, 2001
MathSciNet review: 1838791
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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 [Enhancements On Off] (What's this?)

  • 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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Additional Information

S. M. Malamud
Affiliation: Department of Mathematics, Donetsk State University, Universitetskaya str. 24, Donetsk 340055, Ukraine

Keywords: Integral inequalities on the line
Received by editor(s): September 14, 1998
Received by editor(s) in revised form: January 12, 2000
Published electronically: February 15, 2001
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2001 American Mathematical Society

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