Extremal Approximately Convex Functions and the Best Constants in a Theorem of Hyers and Ulam
| dc.creator | Dilworth, S. J. | |
| dc.creator | Howard, Ralph | |
| dc.creator | Roberts, James W. | |
| dc.date | 2000-11-28 | |
| dc.date.accessioned | 2026-07-07T04:38:53Z | |
| dc.date.available | 2026-07-07T04:38:53Z | |
| dc.description | Let $n\ge1$ and $B\ge2$. A real-valued function $f$ defined on the $n$-simplex $Δ_n$ is approximately convex with respect to $Δ_{B-1}$ iff f(\sum_{i=1}^B t_ix_i) \le \sum_{i=1}^B t_if(x_i) +1 for all $x_1,...,x_B \in Δ_n$ and all $(t_1,...,t_B)\in Δ_{B-1}$. We determine explicitly the extremal (i.e. pointwise largest) function of this type which vanishes on the vertices of $Δ_n$. We also prove a stability theorem of Hyers-Ulam type which yields as a special case the best constants in the Hyers-Ulam stability theorem for $ε$-convex functions. | |
| dc.description | 12 pages 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0011239 | |
| dc.identifier | http://arxiv.org/abs/math/0011239 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60456 | |
| dc.subject | Functional Analysis | |
| dc.subject | Metric Geometry | |
| dc.subject | 26B25; 41A44 | |
| dc.title | Extremal Approximately Convex Functions and the Best Constants in a Theorem of Hyers and Ulam | |
| dc.type | text |