In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series numbers. The mean, or Kolmogorov–Nagumo generalizes the classical mean and appears in many disciplines, from information theory to physics, economics traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introd...

This article investigates the soft-interior (se) and the soft-cover (sc) of operator ideals. These operations, and especially the first one, have been widely used before, but making their role explicit and analyzing their interplay with the arithmetic mean operations is essential for the study in [10] of the multiplicity of traces. Many classical ideals are “soft”, i.e., coincide with their sof...

In this paper we study the average distance in weighted graphs. More precisely, we consider assignments of families of non-negative weights to the edges. The aim is to maximise (minimise, respectively) the average distance in the resulting weighted graph. Two variants of the problem are considered depending on whether the collection of weights is fixed or not. The main results of this paper are...