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Related papers: Inequalities on Geometrically Convex Functions

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The entropy power inequality, which plays a fundamental role in information theory and probability, may be seen as an analogue of the Brunn-Minkowski inequality. Motivated by this connection to Convex Geometry, we survey various recent…

Information Theory · Computer Science 2020-02-07 Mokshay Madiman , James Melbourne , Peng Xu

In this paper we show how the superquadratic functions can be used as a tool for researching other types of convex functions like $\phi $-convexity, strong-convexity and uniform convexity. We show how to use inequalities satisfied by…

Functional Analysis · Mathematics 2024-08-15 Shoshana Abramovich

We study various convex functions on $R^n$ associated with positive definite matrices. This yiels some exotic Holder matrix inequalities.

Functional Analysis · Mathematics 2019-09-27 Jean-Christophe Bourin , Jingjing Shao

We prove capacity inequalities involving the total mean curvature of hypersurfaces with boundary in convex cones and the mass of asymptotically flat manifolds with non-compact boundary. We then give the analogous of P\"olia-Szeg\"o,…

Differential Geometry · Mathematics 2018-08-31 C. Tiarlos Cruz

We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces…

Differential Geometry · Mathematics 2018-10-30 Misha Gromov

In this paper, we establish various inequalities for some mappings that are linked with the illustrious Hermite-Hadamard integral inequality for mappings whose absolute values belong to the class K?;s m;1 and K?;s m;2.

Classical Analysis and ODEs · Mathematics 2013-08-20 Muhammad Muddassar , Ahsan Ali

This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…

Functional Analysis · Mathematics 2014-02-26 Jean-Christophe Bourin , Eun-Young Lee

It is well-known that every convex function admits an affine support at every interior point of a domain. Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree…

Functional Analysis · Mathematics 2008-07-28 Szymon Wasowicz

In this paper, we establish Hermite-Hadamard inequality for interval-valued convex function on the co-ordinates on the rectangle from the plane. We also present Hermite-Hadamard inequality for the product of interval-valued convex functions…

Functional Analysis · Mathematics 2019-12-30 Dafang Zhao , Muhammad Aamir Ali , Ghulam Murtaza

Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give…

Complex Variables · Mathematics 2024-09-12 Rosemarie Bongers

Symmetric powers of quasi-projective schemes can be extended, in terms of left Kan extensions, to geometric symmetric powers of motivic spaces. In this paper, we study geometric symmetric powers and compare with various symmetric powers in…

Algebraic Geometry · Mathematics 2015-04-16 Joe Palacios Baldeon

We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…

Optimization and Control · Mathematics 2019-05-13 James V. Burke , Yuan Gao , Tim Hoheisel

We construct sense-preserving univalent harmonic mappings which map the unit disk onto a domain which is convex in the horizontal direction, but with varying dilatation. Also, we obtain minimal surfaces associated with such harmonic…

Complex Variables · Mathematics 2015-08-04 YuePing Jiang , ZhiHong Liu , Saminathan Ponnusamy

We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an…

Functional Analysis · Mathematics 2011-03-31 Sergey Bobkov , Mokshay Madiman

We introduce and investigate the concept of harmonical $h$-convexity for interval-valued functions. Under this new concept, we prove some new Hermite-Hadamard type inequalities for the interval Riemann integral.

General Mathematics · Mathematics 2020-02-10 Dafang Zhao , Tianqing An , Guoju Ye , Delfim F. M. Torres

In this paper, we first prove two new identities for multiplicative differentiable functions. Based on this identity, we establish a midpoint and trapezoid type inequalities for multiplicatively convex functions. Applications to special…

Classical Analysis and ODEs · Mathematics 2022-08-02 Berhail Amel , Meftah Badreddine

In this paper some Hadamard-type inequalities for convex functions of 3-variables on a rectanguler box are given. We also define a mapping related to convex functions on a rectanguler box.

Classical Analysis and ODEs · Mathematics 2011-04-01 M. E. Ozdemir , Ahmet Ocak Akdemir

In this paper, we establish two new convex dominated function and then we obtain new Hadamard type inequalities related to this denitions.

Classical Analysis and ODEs · Mathematics 2012-02-10 M. Emin Ozdemir , Mevlut Tunc , Havva Kavurmaci

Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all…

Combinatorics · Mathematics 2007-05-23 Helmut Prodinger

In this paper, approximate lower and upper Hermite--Hadamard type inequalities are obtained for functions that are approximately convex with respect to a given Chebyshev system.

Classical Analysis and ODEs · Mathematics 2012-12-06 Judit Makó , Zsolt Páles