Several symmetry problems are discussed. These include the Pompeiu problem and similar conjectures for the heat and wave equations.

A model of coherent upper conditional prevision for bounded random variables is proposed in a metric space. It is defined by the Choquet integral with respect to Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension. Otherwise, when the conditioning event has Hausdorff outer measure equal to zero or infinity in its Hausdorff...

Correspondence: [email protected] Graduate School of Science and Engineering, Yamaguchi University, 755-8611 Une, Japan Full list of author information is available at the end of the article Abstract In this paper, we give a Heisenberg type or a Schrödinger-type uncertainty relation for generalized metric adjusted skew information or generalized metric adjusted correlation measure. These...

We deal with the problem of minimizing the expectation of a real valued random function over the weakly Pareto or Pareto set associated with a Stochastic MultiObjective Optimization Problem (SMOP) whose objectives are expectations of random functions. Assuming that the closed form of these expectations is difficult to obtain, we apply the Sample Average Approximation method (SAA-N, where N is t...

Given a compact metric space (Ω, d) equipped with a non-atomic, probability measure m and a real, positive decreasing function ψ we consider a ‘natural’ class of lim sup subsets Λ(ψ) of Ω. The classical lim sup sets of ‘well approximable’ numbers in the theory of metric Diophantine approximation fall within this class. We show that m(Λ(ψ)) > 0 under a ‘global ubiquity’ hypothesis and the diverg...

In this paper we explore two constructions of the same family of metric measure spaces. The first construction was introduced by Laakso in 2000 where he used it as an example that Poincaré inequalities can hold on spaces of arbitrary Hausdorff dimension. This was proved using minimal generalized upper gradients. Following Cheeger’s work these upper gradients can be used to define a Sobolev spac...

We investigate the topological and metric properties of attractors of an iterated function system (IFS) whose functions may not be contractive. We focus, in particular, on invertible IFSs of finitely many maps on a compact metric space. We rely on ideas of Kieninger [Iterated Function Systems on Compact Hausdorff Spaces (Shaker, Aachen, 2002)] and McGehee and Wiandt [‘Conley decomposition for c...

Let Y be an absolute neighbourhood retract (ANR) for the class of metric spaces and let X be a Hausdorff space. Let Y X denote the space of continuous maps from X to Y equipped with the compact open topology. It is shown that if X is a CW complex then Y X is an ANR for the class of metric spaces if and only if Y X is metrizable and has the homotopy type of a CW complex. The same holds also when...

in this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in cat(0) spaces as well as in uced banach spaces. moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...