Some complex vector systems of partial functional equations
In this paper some types of complex vector systems of partial linear and non-linear functional equations are solved.
Some Functional Inequalities.
Some functional inequalities and their Baire category properties.
Some functional inequalities and their Baire category properties. (Summary).
Stability of an additive-quadratic functional equation of two variables in F-spaces.
Stability of functional inequalities with Cauchy-Jensen additive mappings.
Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities
Let ϕ be an arbitrary bijection of . We prove that if the two-place function is subadditive in then must be a convex homeomorphism of . This is a partial converse of Mulholland’s inequality. Some new properties of subadditive bijections of are also given. We apply the above results to obtain several converses of Minkowski’s inequality.
Subadditive functions on modules and subgroups of abelian groups.
Sur les paires d'équations pré-Schröder et leur équivalence
Pairs of functional pre-Schröder equations (Sₙ) are considered. We show that under some assumptions the system of two equations (S₃), (Sₙ) for some n ≥ 4 is equivalent to the system of all equations (Sₙ) for n ≥ 2. The results answer a question of Gy. Targonski [5] in a particular case.
The additive approximation on a four-variate Jensen-type operator equation.
The stability of the equation on groups.
The structure of disjoint iteration groups on the circle
The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle , that is, families of homeomorphisms such that and each either is the identity mapping or has no fixed point ( is an arbitrary -divisible nontrivial (i.e., ) abelian group).
Über die Funktionalungleichung f(x +y) + f(xy) ... f(x) + f(y) + f(x)f(y).
Weighted entropies
We present an axiomatic characterization of entropies with properties of branching, continuity, and weighted additivity. We deliberately do not assume that the entropies are symmetric. The resulting entropies are generalizations of the entropies of degree α, including the Shannon entropy as the case α = 1. Such “weighted” entropies have potential applications to the “utility of gambling” problem.