On the reverse Orlicz Busemann–Petty centroid inequality
نویسندگان
چکیده
منابع مشابه
On the Reverse L-busemann-petty Centroid Inequality
The volume of the Lp-centroid body of a convex body K ⊂ Rd is a convex function of a time-like parameter when each chord of K parallel to a fixed direction moves with constant speed. This fact is used to study extrema of some affine invariant functionals involving the volume of the Lp-centroid body and related to classical open problems like the slicing problem. Some variants of the Lp-Busemann...
متن کاملOrlicz Centroid Bodies
The sharp affine isoperimetric inequality that bounds the volume of the centroid body of a star body (from below) by the volume of the star body itself is the Busemann-Petty centroid inequality. A decade ago, the Lp analogue of the classical BusemannPetty centroid inequality was proved. Here, the definition of the centroid body is extended to an Orlicz centroid body of a star body, and the corr...
متن کاملAn inequality in Orlicz function spaces with Orlicz norm
We use Simonenko quantitative indices of an N -function Φ to estimate two parameters qΦ and QΦ in Orlicz function spaces L [0,∞) with Orlicz norm, and get the following inequality: BΦ BΦ−1 ≤ qΦ ≤ QΦ ≤ AΦ Aφ−1 , where AΦ and BΦ are Simonenko indices. A similar inequality is obtained in L[0, 1] with Orlicz norm.
متن کاملThe L-busemann-petty Centroid Inequality
The ratio between the volume of the p-centroid body of a convex body K in Rn and the volume of K attains its minimum value if and only if K is an origin symmetric ellipsoid. This result, the Lp-Busemann-Petty centroid inequality, was recently proved by Lutwak, Yang and Zhang. In this paper we show that all the intrinsic volumes of the p-centroid body of K are convex functions of a time-like par...
متن کاملOn a New Reverse Hilbert\'s Type Inequality
In this paper, by using the Euler-Maclaurin expansion for the Riemann-$zeta$ function, we establish an inequality of a weight coefficient. Using this inequality, we derive a new reverse Hilbert's type inequality. As an applications, an equivalent form is obtained.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2011
ISSN: 0196-8858
DOI: 10.1016/j.aam.2011.04.002