Fenchel's inequality
WebAbstract. In this paper we first establish an optimal Sobolev-type inequality for hypersurfaces in Hn H n (see Theorem 1.1). As an application we obtain hyperbolic Alexandrov-Fenchel inequalities for curvature integrals and quermassintegrals. More precisely, we prove a geometric inequality in the hyperbolic space Hn H n, which is a … WebFeb 18, 2024 · New dynamic Hilbert-type inequalities in two independent variables involving Fenchel–Legendre transform. A. El-Deeb, S. Rashid, Z. Khan, S. Makharesh. Mathematics. 2024. In this paper, we establish some dynamic Hilbert-type inequalities in two independent variables on time scales by using the Fenchel–Legendre transform.
Fenchel's inequality
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WebUniversity of British Columbia WebSep 1, 2024 · The Bochner method was already used in [20] to provide new proofs of the Alexandrov-Fenchel inequality, a much deeper result of which (1.6) is a special case, and of the Alexandrov mixed ...
WebIn this paper, we first give two versions of the Fenchel duality formula and Brøndsted-Rockafellar's theorem. The versions are useful and the proofs are not so difficult. Next, we present a theorem in a Banach space to reconsider the Ekeland variational principle and Takahashi's nonconvex minimization theorem proved in a complete metric space. WebFenchel inequality follows from the Brunn-Minkowski inequality. We do not provide here an alternative proof for the Alexandrov-Fenchel inequality in two dimensions. Thus, …
WebSep 9, 2015 · As per Fenchel-Young inequality: \begin{equation} f(x)+f^*(u) \geq \langle x,u \rangle \end{equation} ... Stack Exchange Network Stack Exchange network consists of … WebThe Alexandrov–Fenchel inequality, ... Numerous geometric inequalities, such as the Brunn–Minkowski inequality for convex bodies and Minkowski's first inequality, are …
WebFeb 4, 2024 · The question is about whether two definitions of a dual norm are equivalent for certain norms, and whether the Fenchel-Young inequality holds for the second …
WebFeb 1, 2024 · For related relative isoperimetric inequalities and the Alexandrov-Fenchel inequalities, see for instance [9,11,13,22,37, 48, 59] etc. Recently in [48] Scheuer-Wang-Xia introduced the definition ... five holding constantahttp://staff.ustc.edu.cn/~yongwei/folder/AW_ICCM2024.pdf can i print a passport application form ukWebity and Fenchel- Young’s inequality. Also we have investigated the a ect of product and convolution of two functions on the Young’s inequalities. ACKNOWLEDGEMENT I would like to express my deep sense of gratitude and respect to my supervisor Dr. S. five history facts about the crow tribeWebFenchel’s Duality Theorem By the Fenchel-Young Inequality we know that H(u) + R(Ku) hq;ui+ hp;Kui H (q) R (p) for all p;q. Now choose q = KT p to obtain H(u) + R(Ku) H ( KT … five historical places in ghanaWebNov 8, 2024 · The Alexandrov-Fenchel inequality, a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes, lies at the heart of convex geometry. The characterization of its extremal bodies is a long-standing open problem that dates back to Alexandrov's original 1937 paper. The known extremals already form a … five holding lista firmecan i print a passport application formWebIn particular, the de nition of f yields the following (Young-Fenchel inequality) f(x) xy f(y); (6.2) where the last inequality holds for any y. Using the notion of convex conjugate, we obtain a variational representation of f-divergence in ... Note: The inequality (6.8) can be interpreted as follows: On the left hand side of the inequality we ... five hit songs