随机定向收缩及其应用<sup>*</sup>

随机定向收缩及其应用^*

基金项目: * 中国科学院科学基金资助的课题

摘要: 作为Altman的定向收缩理论^[4,5]和Lee,Padgett的随机收缩理论^[1,2]的推广,本文对非线性集值随机算子引入了随机定向收缩概念,利用这一新概念和超限归纳法,我们证明了非线性集值随机算子方程随机解的几个存在性定理.这些定理分别改进和推广了[1,2,4,5,11]中相应的结果.其次,给出了我们的结果对非线性随机积分和微分方程的某些应用.

Abstract: In this paper, as the generalizations of Altman's directional contractors^[4,5] and Lee and Padgett's random contractors^[1,2] we introduce the concept of random directional contractors for set-valued random operators. Using the new concept and transfinite induction, we show several existence theorems to solutions of nonlinear set-valued random operator equations. Our theorems improve and generalize the corresponding results in [1,2,4,5,11]. Next, some applications of our results to nonlinear random integral and differential equations are given.

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