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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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203205366 |
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| _version_ | 1832552201379119104 |
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| author | Aliasghar Alikhani-Koopaei |
| author_facet | Aliasghar Alikhani-Koopaei |
| author_sort | Aliasghar Alikhani-Koopaei |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0aac9bca99144c1ea92b3c8823649f96 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0aac9bca99144c1ea92b3c8823649f962025-02-03T05:59:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003392465247310.1155/S0161171203205366On common fixed points, periodic points, and recurrent points of continuous functionsAliasghar Alikhani-Koopaei0Berks-Lehigh Valley College, Pennsylvania State University, Reading 19610-6009, PA, USAIt 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.http://dx.doi.org/10.1155/S0161171203205366 |
| spellingShingle | Aliasghar Alikhani-Koopaei On common fixed points, periodic points, and recurrent points of continuous functions International Journal of Mathematics and Mathematical Sciences |
| title | On common fixed points, periodic points, and recurrent points of continuous functions |
| title_full | On common fixed points, periodic points, and recurrent points of continuous functions |
| title_fullStr | On common fixed points, periodic points, and recurrent points of continuous functions |
| title_full_unstemmed | On common fixed points, periodic points, and recurrent points of continuous functions |
| title_short | On common fixed points, periodic points, and recurrent points of continuous functions |
| title_sort | on common fixed points periodic points and recurrent points of continuous functions |
| url | http://dx.doi.org/10.1155/S0161171203205366 |
| work_keys_str_mv | AT aliasgharalikhanikoopaei oncommonfixedpointsperiodicpointsandrecurrentpointsofcontinuousfunctions |