Accession Number : AD0771602

Title :   Two Generalizations of Muirhead's Theorem,

Corporate Author : FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

Personal Author(s) : Proschan,F. ; Sethuraman,J.

Report Date : NOV 1972

Pagination or Media Count : 11

Abstract : Muirhead's theorem states that M(u, x) > or = M(u, y) whenever x majorizes y, u is a positive vector, and M(u, x) is defined to be the summation (pi belongs to S sub n) of (u sup x1, sub pi 1)...(u sup xn, sub pi n), where (S sub n) is the group of all permutations pi of (1, 2,...,n). In the note, Muirhead's theorem is generalized by replacing (u sup z, sub 1) by a function pi(i, z) which is log convex in z. The generalization of Muirhead's theorem to the continuous case by Ryff (1967) in the Pacific Journal of Mathematics is likewise generalized. (Author)

Descriptors :   *Inequalities, *Vector spaces, Integral transforms, Convex sets, Permutations, Theorems, Measure theory

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE