上半连续集值函数的区间迭代

数学物理学报 ›› 2016, Vol. 36 ›› Issue (2): 231-243.

上半连续集值函数的区间迭代

张萍萍¹, 李林²

1. 滨州学院数学系山东滨州 256600;
2. 嘉兴学院数理与信息工程学院浙江嘉兴 314001

收稿日期:2015-09-13 修回日期:2016-02-03 出版日期:2016-04-25 发布日期:2016-04-25
通讯作者: 李林,mathll@163.com E-mail:mathll@163.com
作者简介:张萍萍,zhangpingpingmath@163.com
基金资助:
国家自然科学基金(11301226);山东省自然科学基金(ZR2014AL003);浙江省自然科学基金(LQ13A010017)和山东省科技计划项目(J12L59)资助

Iteration of Upper Semi-Continuous Multifunctions on Interval

Zhang Pingping¹, Li Lin²

1 Department of Mathematics, Binzhou University, Shandong Binzhou 256600;
2 Department of Mathematics, Physics and Information Engineering, Jiaxing University, Zhejiang Jiaxing 314001

Received:2015-09-13 Revised:2016-02-03 Online:2016-04-25 Published:2016-04-25
Supported by:
Supported by the NSFC (11301226), the Shandong Provincial Natural Science Foundation (ZR2014AL003), the Zhejiang Provincial Natural Science Foundation (LQ13A010017) and the Scientific Research Fund of Shandong Provincial Education Department (J12L59)

摘要/Abstract

摘要：

针对定义在紧区间的上半连续集值函数,该文研究一个集值点的集值函数迭代规律.利用该函数在子区间上的严格单调性,给出集值点的位置与其n次迭代式之间的关系.这种方法不仅能得到有限个集值点的上半连续函数迭代规律,同样也适用于定义在实数域上的上半连续集值函数.

关键词: 迭代, 集值函数, 上半连续, 集值点, 单调性

Abstract:

In this paper we study a class of upper semi-continuous multifunctions with a unique set-valued point on compact interval. By classifying the monotonicity on each subinterval, we give a completed relation between the coordinate of the set-valued points and their n-th iteration. Moreover, our method is available for the upper semi-continuous multifunctions with finitely many set-valued points, as well as those ones defined on the whole real line.

Key words: Iteration, Multifunction, Upper semi-continuous, Set-valued point, Monotonicity

中图分类号:

O171

张萍萍, 李林. 上半连续集值函数的区间迭代[J]. 数学物理学报, 2016, 36(2): 231-243.

Zhang Pingping, Li Lin. Iteration of Upper Semi-Continuous Multifunctions on Interval[J]. Acta mathematica scientia,Series A, 2016, 36(2): 231-243.

参考文献

[1] Aubin J P, Fracnkowska H. Set-valued Analysis. Boston:Birkhazuser, 1990
[2] Choi C S, Nam D G. Interpolation for partly hidden diffusion processes. Stochastic Process Appl, 2004, 113:199-216
[3] Hu S, Papageorgiou N S. Handbook of Multivalued Analysis. Dordrecht:Kluwer Academic, 1997
[4] Jarczyk W, Zhang W. Also multifunctions do not like iterative roots. Elemente Math, 2007, 62(2):73-80
[5] Johansson K H, Rantzer A, Aström K J. Fast switches in relay feedback system. Automatica, 1999, 35:539-552
[6] Katok A, Hasselblatt B. Dynamics:A First Course with a Panorama of Recent Develpments. Cambridge:Cambridge University Press, 2003
[7] Kobza J. Iterative functional equation x(x(t))=f(t) with f(t) piecewise linear. J Comput Appl Math, 2002, 115:331-347
[8] Kuczma M. Functional Equations in a Single Variable. Warsaw:PWN-Polish Scientific Publisher, 1968
[9] Kuczma M, Choczewski B, Ger R. Iterative Functional Equations. Cambridge:Cambridge University Press, 1990
[10] Lawry J. A framework for linguistic modelling. Artificial Intelligence, 2004, 155:1-39
[11] Li L, Jarczyk J, Jarczyk W, Zhang W. Iterative roots of mappings with a unique set-value point. Publ Math Debrecen, 2009, 75:203-220
[12] Li L, Zhang W. Construction of usc solutions for a multivalued iterative equation of order n. Results Math, 2012, 62:203-216
[13] Nikodem K, Zhang W. On a multivalued iterative equation. Publ Math Debrecen, 2004, 64:427-435
[14] Rice R E, Schweizer B, Sklar A. When is f(f(z))=az²+bz+c?. Amer Math Monthly, 1980, 87:252-263
[15] Starr R M. General Equilibrium Theory. Cambridge:Cambridge University Press, 1997
[16] Xu B, Nikodem K, Zhang W. On a multivalued iterative equation of order n. J Convex Analysis, 2011, 3:673-686
[17] Zhang J, Yang L, Zhang W. Some advances on functional equations. Adv Math Chin, 1995, 26:385-405
[18] Zhang W. PM functions, their characteristic intervals and iterative roots. Ann Polon Math, 1997, 65:119-128
[19] Zhang W, Zhang W. Computing iterative roots of polygonal functions. J Comp Appl Math, 2007, 205:497-508