On common fixed points, periodic points, and recurrent points of continuous functions
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...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203205366 |
| Summary: | 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]):Fm(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 ωf studied by Bruckner and Ceder and show that the set of recurrent points of such functions are closed intervals. |
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| ISSN: | 0161-1712 1687-0425 |