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Implications between approximate convexity properties and approximate Hermite-Hadamard inequalities

Judit Makó, Zsolt Páles (2012)

Open Mathematics

The connection between the functional inequalities f x + y 2 ⩽ f x + f y 2 + α J x - y , x , y ∈ D , and ∫ 0 1 f t x + 1 - t y ρ t d t ⩽ λ f x + 1 - λ f y + α H x - y , x , y ∈ D , is investigated, where D is a convex subset of a linear space, f: D → ℝ, α H;α J: D-D → ℝ are even functions, λ ∈ [0; 1], and ρ: [0; 1] →ℝ+ is an integrable nonnegative function with ∫01 ρ(t) dt = 1.

Inégalité de Brunn-Minkowski-Lusternik, et autres inégalités géométriques et fonctionnelles

Bernard Maurey (2003/2004)

Séminaire Bourbaki

La théorie des corps convexes a commencé à la fin du xixe siècle avec l’inégalité de Brunn, généralisée ensuite sous la forme de l’inégalité de Brunn-Minkowski-Lusternik, qui s’applique à des ensembles non convexes. Ce thème a depuis longtemps des contacts avec les problèmes isopérimétriques et avec des inégalités d’Analyse telle que les plongements de Sobolev. On développera quelques aspects plus récents des inégalités géométriques, dont certains sont liés à la technique du transport de mesure,...

Informazione relativa in uno spazio con legge d'indipendenza qualsiasi.

Carla Poggi (1982)

Stochastica

The notion of relative measure of information in an abstract information space with generalized independence law is studied. The axiomatic definition is given and the form of dependence on the absolute measures is determined, as a solution of a system of functional equations.

Initial data stability and admissibility of spaces for Itô linear difference equations

Ramazan Kadiev, Pyotr Simonov (2017)

Mathematica Bohemica

The admissibility of spaces for Itô functional difference equations is investigated by the method of modeling equations. The problem of space admissibility is closely connected with the initial data stability problem of solutions for Itô delay differential equations. For these equations the p -stability of initial data solutions is studied as a special case of admissibility of spaces for the corresponding Itô functional difference equation. In most cases, this approach seems to be more constructive...

Instanton-anti-instanton solutions of discrete Yang-Mills equations

Volodymyr Sushch (2012)

Mathematica Bohemica

We study a discrete model of the S U ( 2 ) Yang-Mills equations on a combinatorial analog of ℝ 4 . Self-dual and anti-self-dual solutions of discrete Yang-Mills equations are constructed. To obtain these solutions we use both the techniques of a double complex and the quaternionic approach.

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