成凱歌

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有平頂區(qū)間的遞增自映射迭代

成凱歌

(浙江旅游職業(yè)學(xué)院基礎(chǔ)部，浙江，杭州 311231)

具有平頂區(qū)間的自映射反映了客觀事物在變化過程中某個階段是處于穩(wěn)定狀態(tài)的。研究了具有一個平頂區(qū)間的連續(xù)遞增自映射的迭代問題。討論了這類連續(xù)自映射經(jīng)過迭代后的變化規(guī)律，其所得結(jié)果不僅指出了在迭代過程中平臺區(qū)間和平臺高度是如何變化的，而且為尋求帶平臺的單調(diào)連續(xù)自映射的迭代根提供了思路。

連續(xù)單調(diào)自映射；非單調(diào)點；平頂區(qū)間；不動點；迭代

0 引言

1 預(yù)備知識

2 主要結(jié)果及討論過程

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[2] M C Zdun. On iterative roots of homeomorphisms of the circle [J]. Bull. Pol. Acad. Sci. Math., 2000, 48(2): 203-213.

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[4] Narayaninsamy T. Fractional iterates for piecewise differentiable maps [J]. Appl. Math. Comput., 2007, 192(1): 273-278.

[6] Lesniak Z. On fractional iterates of a Brouwer homeomorphism embeddable a flow [J]. J. Math. Anal. Appl., 2010, 366(1): 310-318.

[7] 程偉博，劉世君. 一類迭代函數(shù)方程解的存在性[J]. 重慶工商大學(xué)學(xué)報:自然科學(xué)版, 2012, 29(7): 36-37.

[8] 李春曄. 集值映射迭代根的不存在性[J]. 成都信息工程學(xué)院學(xué)報, 2010, 25（2）: 221-222.

[9] 毛 冉. 動力系統(tǒng)點集次的迭代不變性[J]. 重慶工商大學(xué)學(xué)報:自然科學(xué)版, 2011, 28(6): 558-563.

[10] 石勇國, 陳麗. 分式線性函數(shù)的亞純迭代根[J]. 中國科學(xué)(A輯, 數(shù)學(xué)), 2009, 39: 121-128.

[11] 陳勝蘭, 方長杰. 變分不等式的新超梯度迭代法[J]. 四川師范大學(xué)學(xué)報:自然科學(xué)版, 2012, 1: 12-15.

ITERATION OF INCREASING SELF-MAPPING WITH LEVEL-TOP INTERVALS

CHENG Kai-ge

(Department of Social Sciences, Tourism College of Zhejiang, Hangzhou, Zhejiang 311231, China)

The self-mapping with level-top intervals reflects the steady state of a stage in the process of objective change. We study the iteration of continuous and increasing self-mapping with one level-top interval and one strictly increasing interval. Furthermore, we discuss the changing regulations of their level-top interval under iteration. The results not only point out that how to change the level-top intervals and level-top heights under iteration, but also show the ideas to find the iterative roots of continuous and monotonic self-mapping with one level-top interval.

continuous and monotonic self-mapping; non-monotone point; level-top interval; the fixed point; iteration

1674-8085(2013)02-0020-05

O193

A

10.3969/j.issn.1674-8085.2013.02.004

2012-09-26；

2013-01-28

成凱歌(1968-)，男，浙江杭州人，講師，主要從事單調(diào)函數(shù)的研究(E-mail: ckg0571@sina. com).