On the best constants associated with n-distances

in Acta Mathematica Hungarica (2020), 161(1), 341-365

We pursue the investigation of the concept of n-distance, an n-variable version of the classical concept of distance recently introduced and investigated by Kiss, Marichal, and Teheux. We especially focus ... [more ▼]

We pursue the investigation of the concept of n-distance, an n-variable version of the classical concept of distance recently introduced and investigated by Kiss, Marichal, and Teheux. We especially focus on the challenging problem of computing the best constant associated with a given n-distance. In particular, we define and investigate the best constants related to partial simplex inequalities. We also introduce and discuss some subclasses of n-distances defined by considering some properties. Finally, we discuss an interesting link between the concepts of n-distance and multidistance. [less ▲]

Barycentrically associative and preassociative functions

in Acta Mathematica Hungarica (2015), 145(2), 468-488

We investigate the barycentric associativity property for functions with indefinite arities and discuss the more general property of barycentric preassociativity, a generalization of barycentric ... [more ▼]

We investigate the barycentric associativity property for functions with indefinite arities and discuss the more general property of barycentric preassociativity, a generalization of barycentric associativity which does not involve any composition of functions. We also provide a generalization of Kolmogoroff-Nagumo's characterization of the quasi-arithmetic mean functions to barycentrically preassociative functions. [less ▲]

Universal distribution of limit points

in Acta Mathematica Hungarica (2011), 133(3), 288-303

We consider sequences of functions that have in some sense a universal distribution of limit points of zeros in the complex plane. In particular, we prove that functions having universal approximation ... [more ▼]

We consider sequences of functions that have in some sense a universal distribution of limit points of zeros in the complex plane. In particular, we prove that functions having universal approximation properties on compact sets with connected complement automatically have such a universal distribution of limit points. Moreover, in the case of sequences of derivatives, we show connections between this kind of universality and some rather old results of Edrei/MacLane and Pólya. Finally, we show the lineability of the set of what we call Jentzsch-universal power series. [less ▲]