不连续随机算子随机不动点定理及其应用

数学物理学报 ›› 2010, Vol. 30 ›› Issue (2): 542-547.

不连续随机算子随机不动点定理及其应用

李志龙

江西财经大学数学系, 330013

收稿日期:2007-12-25 修回日期:2009-05-25 出版日期:2010-04-25 发布日期:2010-04-25
基金资助:
国家自然科学基金$(10626029,10701040)、江西省自然科学基金 (2009GQS0007)、江西省高校人文社科项目(JJ0946)和江西财经大学项目(JXCDJG0813)资助.

Random Fixed Points Theorem of a Class of Discontinuous Random Operators and Its Application

LI Zhi-Long

Department of Mathematics, Jiangxi |University of Finance and Economics, Nanchang 330013

Received:2007-12-25 Revised:2009-05-25 Online:2010-04-25 Published:2010-04-25
Supported by:
国家自然科学基金$(10626029,10701040)、江西省自然科学基金 (2009GQS0007)、江西省高校人文社科项目(JJ0946)和江西财经大学项目(JXCDJG0813)资助.

摘要/Abstract

摘要：

该文利用半序理论和随机压缩映象原理, 得到了一类不连续随机增算子随机不动点的唯一存在定理. 作为应用,考虑了Rⁿ中含间断项的一阶随机微分积分方程初值问题.

关键词: 不连续随机算子, 随机压缩映象原理, 随机不动点, 随机微分积分方程

Abstract:

By using the order theory and random contracted mapping theorem, the existence and uniqueness of random fixed point for a class of discontinuous random operators is obtained. As an application, the existence of the random solution for the initial value problem of the random differential and integral equations in Rⁿ is established.

Key words: Discontinuous random operator, Random contracting mapping theorem, Random fixed points, Random differentiation and integration equations

中图分类号:

47H10

李志龙. 不连续随机算子随机不动点定理及其应用[J]. 数学物理学报, 2010, 30(2): 542-547.

LI Zhi-Long. Random Fixed Points Theorem of a Class of Discontinuous Random Operators and Its Application[J]. Acta mathematica scientia,Series A, 2010, 30(2): 542-547.

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