EuDML | Browse

Displaying 61 – 72 of 72

Convexity and almost convexity in groups

Witold Jarczyk (2013)

Banach Center Publications

We give a review of results proved and published mostly in recent years, concerning real-valued convex functions as well as almost convex functions defined on a (not necessarily convex) subset of a group. Analogues of such classical results as the theorems of Jensen, Bernstein-Doetsch, Blumberg-Sierpiński, Ostrowski, and Mehdi are presented. A version of the Hahn-Banach theorem with a convex control function is proved, too. We also study some questions specific for the group setting, for instance...

Convexity inequalities for estimating generalized conditional entropies from below

Alexey E. Rastegin (2012)

Kybernetika

Generalized entropic functionals are in an active area of research. Hence lower and upper bounds on these functionals are of interest. Lower bounds for estimating Rényi conditional $α$ -entropy and two kinds of non-extensive conditional $α$ -entropy are obtained. These bounds are expressed in terms of error probability of the standard decision and extend the inequalities known for the regular conditional entropy. The presented inequalities are mainly based on the convexity of some functions. In a certain...

Convexity with given infinite weight sequences.

Zoltán Daróczy, Zsolt Páles (1987)

Stochastica

Convex-like inequality, homogeneity, subadditivity, and a characterization of $L^{p}$ -norm

Janusz Matkowski, Marek Pycia (1995)

Annales Polonici Mathematici

Let a and b be fixed real numbers such that 0 < mina,b < 1 < a + b. We prove that every function f:(0,∞) → ℝ satisfying f(as + bt) ≤ af(s) + bf(t), s,t > 0, and such that $l i m s u p_{t \to 0 +} f (t) \leq 0$ must be of the form f(t) = f(1)t, t > 0. This improves an earlier result in [5] where, in particular, f is assumed to be nonnegative. Some generalizations for functions defined on cones in linear spaces are given. We apply these results to give a new characterization of the $L^{p}$ -norm.

Displaying 61 – 72 of 72

Convexity and almost convexity in groups

Convexity inequalities for estimating generalized conditional entropies from below

Convexity with given infinite weight sequences.

Convex-like inequality, homogeneity, subadditivity, and a characterization of $L^{p}$ -norm

Correction Note to the Paper: On a Functional Equation Related to Families of Exponential Probability Measures

Correction to a paper by Newman and Sheingorn.

Correction to: An asymptotic form of Cauchy's functional equation; Volume 24, 2/3 (1982). (Short Communication).

Correction to "On a functional equation arising from hyperbolic geometry", Volume 21 (1980), 113-116.

Corrigendum to "Continuous solutions of a homogeneous functional equation".

Corrigendum to "Stability aspects of arithmetic functions, II" (Acta Arith. 139 (2009), 131-146)

Criteria for the Regularity of Continuous and Locally Integrable Solutions of a Class of Linear Functional Equations

Cyclic complex vector functional equations.

Currently displaying 61 – 72 of 72