Accession Number : AD0432991


Title :   REVERSAL OF THE LYAPUNOV, HOLDER, AND MINKOWSKI INEQUALITIES AND OTHER EXTENSIONS OF THE KANTOROVECH INEQUALITY,


Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH


Personal Author(s) : Marshall,Albert W ; Olkin,Ingram


Report Date : Feb 1964


Pagination or Media Count : 24


Abstract : Many classical inequalities which involve random variables or functions on a measure space can be reversed if bounds on the random variables or functions are known. This reversal is accomplished by introducing on one side of the inequality an appropriate multiplicative constant which depends on the known bounds. In this paper, several such inequalities are obtained, and a matrix-theoretic interpretation is used to yield various generalizations of Kantorovich's inequality. Some bounds for expectations of convex functions are also given in the multivariate case. (Author)


Descriptors :   *INEQUALITIES , MATRICES(MATHEMATICS) , STATISTICAL ANALYSIS , PROBABILITY , SERIES(MATHEMATICS) , MEASURE THEORY , COMPLEX NUMBERS


Distribution Statement : APPROVED FOR PUBLIC RELEASE