SOME INEQUALITIES FOR STARSHAPED AND CONVEX FUNCTIONS,
Abstract
Necessary and sufficient conditons are obtained on a function G of bounded variation such that phi(integral sign x(t)dG(t)) = or < integral sign phi(x(t))dG(t) for all increasing x for which x(t sub 0) = 0 for some specified t sub 0, and all convex phi for which phi(0) = 0; the conditions are otherwise independent of phi and x. Similar results are obtained when the inequality is reversed. Necessary and sufficient conditions for both directions of inequality are also obtained when phi is starshaped. The relationship to previous results is sketched. Applications to statistical tolerance limits are indicated. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1967
- Accession Number
- AD0660072
Entities
People
- Albert W. Marshall
- Frank Proschan
- Richard E. Barlow
Organizations
- Boeing