Details
| Original language | English |
|---|---|
| Pages (from-to) | 27-34 |
| Number of pages | 8 |
| Journal | Archive for mathematical logic |
| Volume | 58 |
| Issue number | 1-2 |
| Early online date | 22 Feb 2018 |
| Publication status | Published - 5 Feb 2019 |
| Externally published | Yes |
Abstract
We show constructively that every quasi-convex, uniformly continuous function f: C→ R with at most one minimum point has a minimum point, where C is a convex compact subset of a finite dimensional normed space. Applications include a result on strictly quasi-convex functions, a supporting hyperplane theorem, and a short proof of the constructive fundamental theorem of approximation theory.
Keywords
- Approximation theory, Bishop’s constructive mathematics, Convex sets and functions, Supporting hyperplanes
ASJC Scopus subject areas
- Arts and Humanities(all)
- Philosophy
- Mathematics(all)
- Logic
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Archive for mathematical logic, Vol. 58, No. 1-2, 05.02.2019, p. 27-34.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Convexity and unique minimum points
AU - Berger, Josef
AU - Svindland, G.
N1 - Publisher Copyright: © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/2/5
Y1 - 2019/2/5
N2 - We show constructively that every quasi-convex, uniformly continuous function f: C→ R with at most one minimum point has a minimum point, where C is a convex compact subset of a finite dimensional normed space. Applications include a result on strictly quasi-convex functions, a supporting hyperplane theorem, and a short proof of the constructive fundamental theorem of approximation theory.
AB - We show constructively that every quasi-convex, uniformly continuous function f: C→ R with at most one minimum point has a minimum point, where C is a convex compact subset of a finite dimensional normed space. Applications include a result on strictly quasi-convex functions, a supporting hyperplane theorem, and a short proof of the constructive fundamental theorem of approximation theory.
KW - Approximation theory
KW - Bishop’s constructive mathematics
KW - Convex sets and functions
KW - Supporting hyperplanes
UR - http://www.scopus.com/inward/record.url?scp=85042219120&partnerID=8YFLogxK
U2 - 10.1007/s00153-018-0619-2
DO - 10.1007/s00153-018-0619-2
M3 - Article
VL - 58
SP - 27
EP - 34
JO - Archive for mathematical logic
JF - Archive for mathematical logic
SN - 0933-5846
IS - 1-2
ER -