On a conjecture of de La Grandville and Solow concerning power means.
On a geometric property of positive definite matrices cone.
On a linear functional equation with a mean-type mapping having no fixed points
Our aim is to study continuous solutions φ of the classical linear iterative equation φ(f(x,y)) = g(x,y)φ(x,y) + h(x,y), where the given function f is defined as a pair of means. We are interested in the case when f has no fixed points. In turns out that in such a case continuous solutions of (1) depend on an arbitrary function.
On a mean value theorem in the class of Herglotz functions and its applications.
On a new class of distances between fuzzy numbers.
In the course of the studies on fuzzy regression analysis, we encountered the problem of introducing a distance between fuzzy numbers, which replaces the classical (x - y)2 on the real line. Our proposal is to compute such a function as a suitable weighted mean of the distances between the α-cuts of the fuzzy numbers. The main difficulty is concerned with the definition of the distance between intervals, since the current definitions present some disadvantages which are undesirable in our context....
On a problem concerning quasianalytic local rings
Let (ₙ)ₙ be a quasianalytic differentiable system. Let m ∈ ℕ. We consider the following problem: let and f̂ be its Taylor series at . Split the set of exponents into two disjoint subsets A and B, , and decompose the formal series f̂ into the sum of two formal series G and H, supported by A and B, respectively. Do there exist with Taylor series at zero G and H, respectively? The main result of this paper is the following: if we have a positive answer to the above problem for some m ≥ 2, then...
On a problem of Davison.
On absolutely monotone set-valued functions
We define absolutely monotone multifunctions and prove their analyticity on an interval [0,b).
On almost everywhere differentiability of the metric projection on closed sets in ,
Let be a closed subset of and let denote the metric projection (closest point mapping) of onto in -norm. A classical result of Asplund states that is (Fréchet) differentiable almost everywhere (a.e.) in in the Euclidean case . We consider the case and prove that the th component of is differentiable a.e. if and satisfies Hölder condition of order if .
On alternative functional equations. (Short Communication).
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.
On an exponential-type fuzzy difference equation.
On an inequality of Diananda.
On an inequality of Diananda. II.
On an inequality of Diananda. III.
On an integral inequality.
On Aumann's theorem that the circle does not admit a mean
On certain inequalities for means in two variables.
On certain means of two arguments and their extensions.
On Choquet's theory