On common fixed points, periodic points, and recurrent points of continuous functions

Aliasghar Alikhani-Koopaei

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-9

Abstract:

It is known that two commuting continuous functions on an interval need not have a common fixed point. However, it is not known if such two functions have a common periodic point. we had conjectured that two commuting continuous functions on an interval will typically have disjoint sets of periodic points. In this paper, we first prove that S is a nowhere dense subset of [ 0 , 1 ] if and only if { f ∈ C ( [ 0 , 1 ] ) : F m ( f ) ∩ S ¯ ≠ ∅ } is a nowhere dense subset of C ( [ 0 , 1 ] ) . We also give some results about the common fixed, periodic, and recurrent points of functions. We consider the class of functions f with continuous ω f studied by Bruckner and Ceder and show that the set of recurrent points of such functions are closed intervals.

Date: 2003
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2003/634295.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2003/634295.xml (text/xml)

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:hin:jijmms:634295

DOI: 10.1155/S0161171203205366

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().