TY - JOUR

T1 - On common fixed points, periodic points, and recurrent points of continuous functions

AU - Alikhani-Koopaei, Aliasghar

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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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U2 - 10.1155/S0161171203205366

DO - 10.1155/S0161171203205366

M3 - Article

AN - SCOPUS:17844380231

SN - 0161-1712

VL - 2003

SP - 2465

EP - 2473

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

IS - 39

ER -