On Inequalities for Products of Power Sums.
On reduction of linear two variable functional equations to differential equations without substitutions.
On homogeneous quasideviation menas.
On the generalization of quasiarithmetic means with weight function. (Short Communication).
Report of Meeting: The Twent-ninth International Symposium on Functional Equations, June 3 - June 10, 1991, Wolfville, N.S.
On the characterization of quasiarithmetic means with weight function.
General inequalities for quasideviation means.
A Hahn-Banach theorem for separation of semigroups and its application.
Separation via quadratic functions. (Summary).
Separation via quadratic functions.
Implications between approximate convexity properties and approximate Hermite-Hadamard inequalities
The connection between the functional inequalities and 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.
Remarks on the comparison of weighted quasi-arithmetic means
We present comparison theorems for the weighted quasi-arithmetic means and for weighted Bajraktarević means without supposing in advance that the weights are the same.
Minkowski sums of Cantor-type sets
The classical Steinhaus theorem on the Minkowski sum of the Cantor set is generalized to a large class of fractals determined by Hutchinson-type operators. Numerous examples illustrating the results obtained and an application to t-convex functions are presented.
Convexity with given infinite weight sequences.
On an elementary inclusion problem and generalized weighted quasi-arithmetic means
The aim of this note is to characterize the real coefficients p₁,...,pₙ and q₁,...,qₖ so that be valid whenever the vectors x₁,...,xₙ, y₁,...,yₖ satisfy y₁,...,yₖ ⊆ convx₁,...,xₙ. Using this characterization, a class of generalized weighted quasi-arithmetic means is introduced and several open problems are formulated.
Abstract separation theorems of Rodé type and their applications
Sufficient and necessary conditions are presented under which two given functions can be separated by a function Π-affine in Rodé sense (resp. Π-convex, Π-concave). As special cases several old and new separation theorems are obtained.
Report of the General Inequalities 8 Conference September 15--21, 2002, Noszvaj, Hungary.
An example of a stable functional equation when the Hyers method does not work.
Characterizations of inner product spaces by strongly convex functions.
An extension of the Hermite-Hadamard inequality and an application for Gini and Stolarsky means.
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