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
On classification of real singularities.
On completeness of left-invariant Lorentz metrics on solvable Lie groups.
We study geodesic completeness for left-invariant Lorentz metrics on solvable Lie groups.
On continuous convex or concave functions with respect to the logarithmic mean
On convex and *-concave multifunctions
A continuous multifunction F:[a,b] → clb(Y) is *-concave if and only if the inclusion holds for every s,t ∈ [a,b], s < t.
On derivo-periodic multifunctions
The problem of linearity of a multivalued derivative and consequently the problem of necessary and sufficient conditions for derivo-periodic multifunctions are investigated. The notion of a derivative of multivalued functions is understood in various ways. Advantages and disadvantages of these approaches are discussed.
On expanding iteration semigroups of set-valued functions.