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 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 inequality of Diananda.
On an inequality of Diananda. II.
On an inequality of Diananda. III.
On an integral inequality.
On certain inequalities for means in two variables.
On certain means of two arguments and their extensions.
On continuous convex or concave functions with respect to the logarithmic mean
On inequalities for hypergeometric analogues of the arithmetic-geometric mean.
On logarithmic convexity for differences of power means.
On majorization, favard and Berwald inequalities.
On some exponential means. II.
On some geometrical properties of generalized modular spaces of Cesàro type defined by weighted means. (On some geometrical properties of generalized modular spaces of Cesáro type defined by weighted means.)
On some iterated means arising in homogenization theory
We consider iteration of arithmetic and power means and discuss methods for determining their limit. These means appear naturally in connection with some problems in homogenization theory.
On some spectral results relating to the relative values of means.
On the homogeneous functions with two parameters and its monotonicity.