scholarly journals Mixed ƒ-divergence for Multiple Pairs of Measures

2017 ◽  
Vol 60 (3) ◽  
pp. 641-654 ◽  
Author(s):  
Elisabeth Werner ◽  
Deping Ye
Keyword(s):  
Isoperimetric Inequality ◽  
Type Inequality ◽  
Probability Measures ◽  
Permutation Invariance

AbstractIn this paper, the concept of the classical ƒ-divergence for a pair of measures is extended to the mixed ƒ-divergence formultiple pairs ofmeasures. The mixed ƒ-divergence provides a way to measure the diòerence between multiple pairs of (probability) measures. Properties for the mixed ƒ-divergence are established, such as permutation invariance and symmetry in distributions. An Alexandrov–Fenchel type inequality and an isoperimetric inequality for the mixed ƒ-divergence are proved.

POSITIVE CENTRE SETS OF CONVEX CURVES AND A BONNESEN TYPE INEQUALITY

2018 ◽  
Vol 99 (2) ◽  
pp. 293-301
Author(s):  
YUNLONG YANG
Keyword(s):  
Isoperimetric Inequality ◽  
Type Inequality ◽  
Convex Curves

We consider the positive centre sets of regular $n$-gons, rectangles and half discs, and conjecture a Bonnesen type inequality concerning positive centre sets which is stronger than the classical isoperimetric inequality.

scholarly journals Characterization of Low Dimensional RCD*(K, N) Spaces

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Yu Kitabeppu ◽  
Sajjad Lakzian
Keyword(s):  
Hausdorff Dimension ◽  
Isoperimetric Inequality ◽  
Type Inequality ◽  
Metric Measure Spaces ◽  
One Dimensional ◽  
Curvature Bounds ◽  
Measure Spaces ◽  
Low Dimensional ◽  
Regular Sets

AbstractIn this paper,we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called RCD*(K, N) spaces) with non-empty one dimensional regular sets. In particular, we prove that the class of Ricci limit spaces with Ric ≥ K and Hausdorff dimension N and the class of RCD*(K, N) spaces coincide for N < 2 (They can be either complete intervals or circles). We will also prove a Bishop-Gromov type inequality (that is ,roughly speaking, a converse to the Lévy-Gromov’s isoperimetric inequality and was previously only known for Ricci limit spaces) which might be also of independent interest.

scholarly journals A spherical rearrangement proof of the stability of a Riesz-type inequality and an application to an isoperimetric type problem

2021 ◽  
Author(s):  
Giacomo Ascione
Keyword(s):  
Isoperimetric Inequality ◽  
Type Inequality ◽  
Stability Result ◽  
Global Minimizer ◽  
Mass Transportation ◽  
Volume Constraint ◽  
Type Problem ◽  
Fixed Volume ◽  
The Stability ◽  
Perimeter Penalization

We prove the stability of the ball as global minimizer of an attractive shape functional under volume constraint, by means of mass transportation arguments. The stability exponent is $1/2$ and it is sharp. Moreover, we use such stability result together with the quantitative (possibly fractional) isoperimetric inequality to prove that the ball is a global minimizer of a shape functional involving both an attractive and a repulsive term with a sufficiently large fixed volume and with a suitable (possibly fractional) perimeter penalization.

LIFTING THE FUNCTOR ITO THE CATEGORY OF UNIFORM SPACES

2020 ◽  
Vol 4 (1) ◽  
pp. 29-39
Author(s):  
Dilrabo Eshkobilova ◽  
Keyword(s):  
Compact Support ◽  
Probability Measures ◽  
Uniform Spaces ◽  
Continuous Maps ◽  
Uniformly Continuous

Uniform properties of the functor Iof idempotent probability measures with compact support are studied. It is proved that this functor can be lifted to the category Unif of uniform spaces and uniformly continuous maps

On the equicontinuity of families of inverse mappings of Riemannian manifolds

2019 ◽  
Vol 16 (4) ◽  
pp. 557-566
Author(s):  
Denis Ilyutko ◽  
Evgenii Sevost'yanov
Keyword(s):  
Riemannian Manifolds ◽  
Type Inequality ◽  
The Given ◽  
Range Of Values

We study homeomorphisms of Riemannian manifolds with unbounded characteristic such that the inverse mappings satisfy the Poletsky-type inequality. It is established that their families are equicontinuous if the function Q which is related to the Poletsky inequality and is responsible for a distortion of the modulus, is integrable in the given domain, here the original manifold is connected and the domain of definition and the range of values of mappings have compact closures.

New generalized 2D Ostrowski type inequalities on time scales with k2 points using a parameter

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3155-3169 ◽  
Author(s):  
Seth Kermausuor ◽  
Eze Nwaeze
Keyword(s):  
Numerical Analysis ◽  
Time Scales ◽  
Type Inequality ◽  
Dimensional Case ◽  
Multiple Points ◽  
Quantum Calculus ◽  
Independent Variables ◽  
Ostrowski Type Inequality ◽  
Two Independent Variables

Recently, a new Ostrowski type inequality on time scales for k points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with k points. Journal of Mathematical Inequalities (2017), 11(1):41-48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 2012:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.

Sign in / Sign up

Export Citation Format

Share Document