In: Mathematica Slovaca, vol. 64, no. 1
O. Dovgoshey - E. Petrov - G. Kozub
Detaily:
Rok, strany: 2014, 187 - 208
Kľúčové slová:
metric product, isotone metric preserving function of several variables, bornologous function, isotone subadditive function, modulus of continuity
O článku:
Let $\mathbb{R}+=[0,∞)$ and let $A\subseteq\mathbb{R}n+$. We have found the necessary and sufficient conditions under which a function $Φ:A\to\mathbb{R}+$ has an isotone subadditive continuation on $\mathbb{R}n+$. It allows us to describe the metrics, defined on the Cartesian product $X1×…× Xn$ of given metric spaces $(X1,dX1),…,(Xn,dXn)$, generated by the isotone metric preserving functions on $\mathbb{R}n+$. It is also shown that the isotone metric preserving functions $Φ:\mathbb{R}n+\to\mathbb{R}+$ coincide with the first moduli of continuity of the nonconstant bornologous functions $g:\mathbb{R}n+\to\mathbb{R}+$.
Ako citovať:
ISO 690:
Dovgoshey, O., Petrov, E., Kozub, G. 2014. Metric products and continuation of isotone functions. In Mathematica Slovaca, vol. 64, no.1, pp. 187-208. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0195-1
APA:
Dovgoshey, O., Petrov, E., Kozub, G. (2014). Metric products and continuation of isotone functions. Mathematica Slovaca, 64(1), 187-208. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0195-1
O vydaní: