The Hellinger-Kantorovich (HK) distance is an unbalanced extension of the Wasserstein-2 distance. It was shown recently that HK barycenter exhibits a much more complex behaviour than Wasserstein barycenter. Motivated by this observation we study in detail for case where input measures are uncountable collection Dirac measures, particular dependency on length scale parameter HK, question whether...

Abstract The main purpose of this paper is to use a power series summability method study some approximation properties Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya result.

In the present paper we establish a link between Lupa? operators and its Kantorovich type integral modification, by applying methods of finite differences, also difference two is established in weighted spaces. Further, consider modification variant, which preserve test functions evjx,j=1,2 estimate Voronovskaja convergence estimate.

We consider nonlinear Kantorovich problems with marginal distributions and cost functions depending measurably on a parameter prove that there exist optimal transportation plans are also measurable respect to the parameter. Unlike classical linear problem of minimization integrals given function plans, we deal functionals in which integrands depend plans. Dependence conditional measures is allo...