About Some Monge–Kantovorich Type Norm and Their Applications to the Theory of Fractals

Ion Mierluș-Mazilu () and Lucian Niță
Additional contact information
Ion Mierluș-Mazilu: Department of Mathematics and Computer Science, Technical University of Civil Engineering of Bucharest, 020396 Bucharest, Romania
Lucian Niță: Department of Mathematics and Computer Science, Technical University of Civil Engineering of Bucharest, 020396 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 24, 1-14

Abstract: If X is a Hilbert space, one can consider the space cabv ( X ) of X valued measures defined on the Borel sets of a compact metric space, having a bounded variation. On this vector measures space was already introduced a Monge–Kantorovich type norm. Our first goal was to introduce a Monge–Kantorovich type norm on cabv ( X ) , where X is a Banach space, but not necessarily a Hilbert space. Thus, we introduced here the Monge–Kantorovich type norm on cabv L q ( [ 0 , 1 ] ) , ( 1 < q < ∞ ) . We obtained some properties of this norm and provided some examples. Then, we used the Monge–Kantorovich norm on cabv K n ( K being R or C ) to obtain convergence properties for sequences of fractal sets and fractal vector measures associated to a sequence of iterated function systems.

Keywords: variation of a vector measure; Haar functions; attractor; fractal measure; Lipschitz functions; weak convergence of operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/24/4825/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/24/4825/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:24:p:4825-:d:1007719

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().