关于连续函数的公共不动点、周期点和循环点

IF 1 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-12-01 DOI:10.1155/S0161171203205366

A. Alikhani-Koopaei

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引用次数: 6

摘要

已知区间上的两个可交换连续函数不需要有公共不动点。然而，不知道这两个函数是否有一个共同的周期点。我们已经推测出在一个区间上的两个可交换连续函数通常有不相交的周期点集。在本文中，我们首先证明S是[0,1]的一个无处稠密子集当且仅当{f∈C ([0,1]): f m (f)∩S¯≠∅}是C([0,1])的一个无处稠密子集。给出了函数的一般不动点、周期点和循环点的一些结果。考虑Bruckner和Ceder研究的一类具有连续ω f的函数f，并证明了这类函数的循环点集合是闭区间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 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.

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来源期刊

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Mathematics-Mathematics (miscellaneous)

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

17 weeks

期刊介绍： The International Journal of Mathematics and Mathematical Sciences is a refereed math journal devoted to publication of original research articles, research notes, and review articles, with emphasis on contributions to unsolved problems and open questions in mathematics and mathematical sciences. All areas listed on the cover of Mathematical Reviews, such as pure and applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology, are included within the scope of the International Journal of Mathematics and Mathematical Sciences.