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Pech, Pavel
A sharpening of a discrete analog of Wirtinger's and isoperimetric inequalities. (English). Mathematica Bohemica, vol. 117 (1992), issue 4, pp. 425-428
MSC: 51M16, 52A40 | MR 1197291 | Zbl 0773.52005 | DOI: 10.21136/MB.1992.126056
Keywords:
closed $n$-gons; inequalities; Wirtinger's inequality; trigonometric polynomials
Summary:
A sharpening of a discrete case of Wirtinger's inequality is given. It is then used to sharpen the isoperimetric unequality for polygons.
References:
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[2] K. Fan O. Taussky J. Todd: Discrete analogs of inequalities of Wirtinger. Monatsh. Math. 50 (1955), 73-90. MR 0070676
[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
[4] J. Novotná: A sharpening of discrete analogues of Wirtinger's inequality. Čas. pro pěst. mat. 108 (1983), 70-77. MR 0694141 | Zbl 0521.26008
[5] I. J. Schoenberg: The finite Fourier series and elementary geometry. Amer. Math. Monthly 57 (1950), 390-404. DOI 10.1080/00029890.1950.11999555 | MR 0036332 | Zbl 0038.35602
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