| Title:
|
A sharpening of a discrete analog of Wirtinger's and isoperimetric inequalities (English) |
| Author:
|
Pech, Pavel |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
117 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
425-428 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A sharpening of a discrete case of Wirtinger's inequality is given. It is then used to sharpen the isoperimetric unequality for polygons. (English) |
| Keyword:
|
closed $n$-gons |
| Keyword:
|
inequalities |
| Keyword:
|
Wirtinger's inequality |
| Keyword:
|
trigonometric polynomials |
| MSC:
|
51M16 |
| MSC:
|
52A40 |
| idZBL:
|
Zbl 0773.52005 |
| idMR:
|
MR1197291 |
| DOI:
|
10.21136/MB.1992.126056 |
| . |
| Date available:
|
2009-09-24T20:55:46Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126056 |
| . |
| Reference:
|
[1] L. Boček: Isoperimetrische Ungleichungen für räumliche Kurven und Polygone.Čas. pro pěst. mat. 104 (1979), 86-92. MR 0523575 |
| Reference:
|
[2] K. Fan O. Taussky J. Todd: Discrete analogs of inequalities of Wirtinger.Monatsh. Math. 50 (1955), 73-90. MR 0070676 |
| Reference:
|
[3] Z. Nádeník: Die Verchärfung einer Ungleichung von Frobenius für den gemischten Flächeninhalt der konvexen ebenen Bereiche.Čas. pro pěst, mat. 90 (1965), 220-225. MR 0192411 |
| Reference:
|
[4] J. Novotná: A sharpening of discrete analogues of Wirtinger's inequality.Čas. pro pěst. mat. 108 (1983), 70-77. Zbl 0521.26008, MR 0694141 |
| Reference:
|
[5] I. J. Schoenberg: The finite Fourier series and elementary geometry.Amer. Math. Monthly 57 (1950), 390-404. Zbl 0038.35602, MR 0036332, 10.1080/00029890.1950.11999555 |
| . |
