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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Disconjugacy and integral inequalities


Author: Achim Clausing
Journal: Trans. Amer. Math. Soc. 260 (1980), 293-307
MSC: Primary 26D15; Secondary 34B27
MathSciNet review: 570791
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Abstract: The basic data in this paper are a disconjugate differential operator and an associated two-point boundary value problem.

These define in a natural way a cone of functions satisfying a differential inequality with respect to the operator. By using a result of P. W. Bates and G. B. Gustafson on the monotonicity properties of Green's kernels it is shown that such a cone has a compact convex base which is a Bauer simplex. This result is used to derive a variety of integral inequalities which include known inequalities of Frank and Pick, Levin and Steckin, Karlin and Ziegler, as well as several new ones.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0570791-X
PII: S 0002-9947(1980)0570791-X
Keywords: Disconjugate differential operator, differential inequality, monotonicity properties of Green's kernels, integral representation, integral inequality
Article copyright: © Copyright 1980 American Mathematical Society