Generalizations and improvements of converse Jensen's inequality for convex hulls in ℝ^k$
نویسندگان
چکیده
منابع مشابه
JENSEN’S INEQUALITY FOR GG-CONVEX FUNCTIONS
In this paper, we obtain Jensen’s inequality for GG-convex functions. Also, we get in- equalities alike to Hermite-Hadamard inequality for GG-convex functions. Some examples are given.
متن کاملA Converse of the Jensen Inequality for Convex Mappings of Several Variables and Applications
In this paper we point out a converse result of the celebrated Jensen inequality for differentiable convex mappings of several variables and apply it to counterpart well-known analytic inequalities. Applications to Shannon’s and Rényi’s entropy mappings are also given.
متن کاملConvex Hulls for Random Lines
Consider n i .i .d . random lines in the plane defined by their slope and distance from the origin . The slope is uniformly distributed on (0, 27r] and independent of the distance R from the origin . These lines define a set I of n(n 1)/2 intersection points . It was recently shown by Atallah and Ching and Lee that the cardinality of the convex hull of these intersection points is 0(n), and the...
متن کاملConvex hulls of spheres and convex hulls of disjoint convex polytopes
Given a set Σ of spheres in E, with d ≥ 3 and d odd, having a constant number of m distinct radii ρ1, ρ2, . . . , ρm, we show that the worst-case combinatorial complexity of the convex hull of Σ is Θ( ∑ 1≤i6=j≤m nin ⌊ d 2 ⌋ j ), where ni is the number of spheres in Σ with radius ρi. To prove the lower bound, we construct a set of Θ(n1+n2) spheres in E , with d ≥ 3 odd, where ni spheres have rad...
متن کاملFormalizing Convex Hulls Algorithms
We study the development of formally proved algorithms for computational geometry. The result of this work is a formal description of the basic principles that make convex hull algorithms work and two programs that implement convex hull computation and have been automatically obtained from formally verified mathematical proofs. A special attention has been given to handling degenerated cases th...
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: Mathematical Inequalities & Applications
سال: 2014
ISSN: 1331-4343
DOI: 10.7153/mia-17-84