In: Tatra Mountains Mathematical Publications, vol. 58, no. 1
Ewa Korczak-Kubiak - Ryszard J. Pawlak
Detaily:
Rok, strany: 2014, 77 - 89
Kľúčové slová:
trajectory, first return path, fixed point, strong entropy point,
$H_{C}$-connected function, ring of functions, graph of functions, topology of uniform convergence
O článku:
The paper deals with approximation of functions from the unit interval into itself by means of functions having strong entropy point. For this purpose we define a family of functions having the fixed point property: $ConnC$ (which is a subfamily of the class $Conn$ introduced in [Korczak-Kubiak, E., Paw lak, R. J.: \textit{Trajectories, first return limiting notions and rings of $H$-connected and iteratively $H$-connected functions}, Czechoslovak Math. J. \textbf{63} (2013), 679–700]). The main result of the paper is a theorem saying that for any function $f\in ConnC$ and any point $x0\in { Fix}(f)$ there exists a ring $R\subset ConnC$ containing function $f$ and in the intersection of any ``graph neighbourhood of $f$'' and ``neighbourhood of $f$ in topology of uniform convergence'', one can find functions $ξ,ψ \in R$ having a strong entropy point $y0$ located close to the point $x0$ and being a discontinuity point of the function $ξ$ and a continuity point of the function $ψ$.
Ako citovať:
ISO 690:
Korczak-Kubiak, E., Pawlak, R. 2014. On approximation by functions having a strong entropy point. In Tatra Mountains Mathematical Publications, vol. 58, no.1, pp. 77-89. 1210-3195.
APA:
Korczak-Kubiak, E., Pawlak, R. (2014). On approximation by functions having a strong entropy point. Tatra Mountains Mathematical Publications, 58(1), 77-89. 1210-3195.