Some complements to the Jensen and Chebyshev inequalities and a problem of W. Walter
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- by S. M. Malamud PDF
- Proc. Amer. Math. Soc. 129 (2001), 2671-2678 Request permission
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
- P. J. Bushell and W. Okrasiński, Nonlinear Volterra integral equations with convolution kernel, J. London Math. Soc. (2) 41 (1990), no. 3, 503–510. MR 1072055, DOI 10.1112/jlms/s2-41.3.503
- Yu. V. Egorov, On the best constant in a Poincaré-Sobolev inequality, Operator Theory: Advances and Applications (to appear).
- W. Walter, Problem: An integral inequality by Bushell and Okrasínski, Intern. series of Numerical Mathematics Vol. 103 (1992).
- W. Walter and V. Weckesser, An integral inequality of convolution type, Aequationes Math. 46 (1993), no. 3, 212–219. MR 1232043, DOI 10.1007/BF01834008
Additional Information
- S. M. Malamud
- Affiliation: Department of Mathematics, Donetsk State University, Universitetskaya str. 24, Donetsk 340055, Ukraine
- MR Author ID: 193515
- Email: MMM@univ.donetsk.ua
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2671-2678
- MSC (1991): Primary 26D15
- DOI: https://doi.org/10.1090/S0002-9939-01-05849-X
- MathSciNet review: 1838791