<abstract xmlns="http://www.w3.org/1999/xhtml"> 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.: Trajectories, first return limiting notions and rings of H-connected and iteratively H-connected functions. Czechoslovak Math. J. 63 (2013). 679-700]). The main result of the paper Is a theorem saying that for any function ƒ ∈ ConnC and any point x0 ∈ Fix(ƒ) there exists a ring R ⊂ ConnC containing function ƒ and in the intersection of any “graph neighbourhood of ƒ” and “neighbourhood of ƒ in topology of uniform convergence”, one can find functions ξ,Ψ ∈ 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. </abstract>

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.: Trajectories, first return limiting notions and rings of H-connected and iteratively H-connected functions. Czechoslovak Math. J. 63 (2013). 679-700]). The main result of the paper Is a theorem saying that for any function ƒ ∈ ConnC and any point x0 ∈ Fix(ƒ) there exists a ring R ⊂ ConnC containing function ƒ and in the intersection of any “graph neighbourhood of ƒ” and “neighbourhood of ƒ in topology of uniform convergence”, one can find functions ξ,Ψ ∈ 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.

On approximation by Function having a strong Entropy Point

University of Lódž Banacha, 22 PL 90-238 Lódž POLAND

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On approximation by Function having a strong Entropy Point"}

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...

On approximation by Function having a strong Entropy Point

Publié en ligne: 15 août 2014

Pages: 77 - 89

Reçu: 18 nov. 2013

DOI: https://doi.org/10.2478/tmmp-2014-0007

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.