Abstract
We prove ‘power’ generalizations of Marcus–Lopes style (including McLeod and Bullen) concavity inequalities for elementary symmetric polynomials, and similar generalizations to convexity inequalities of McLeod and Baston for complete homogeneous symmetric polynomials. We also present additional concavity results for elementary symmetric polynomials, of which the main result is a concavity theorem that yields a well-known log-convexity 1972 result of Muir for positive definite matrices as a corollary.
| Original language | English |
|---|---|
| Pages (from-to) | 1031-1038 |
| Number of pages | 8 |
| Journal | Linear and Multilinear Algebra |
| Volume | 68 |
| Issue number | 5 |
| DOIs | |
| State | Published - 3 May 2020 |
| Externally published | Yes |
Keywords
- Dresher inequality
- Marcus–Lopes inequality
- Muir inequality
- Ravindra B. Bapat
- concavity
- symmetric polynomials
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