关于一类随机非线性算子方程的若干问题的研究(英文)  

Research on Some Problems of a Class of Random Nonlinear Operator Equations

作　　者：朱传喜[1] 刘建辉[1] 吴照奇[1] 

机构地区：[1]南昌大学数学系,南昌江西330031

出　　处：《数学进展》2015年第2期271-276,共6页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11071108,No.11326099,No.11361042);Natural Science Foundation of Jiangxi province of China(No.2010GZS0147);the Youth Foundation of the Education Department of Jiangxi(No.GJJ13012)

摘　　要：本文推广了两个重要的不等式,并且利用随机不动点指数理论研究了一类随机非线性算子方程的随机解的存在性问题,主要结果推广了著名的Altman定理.最后给出主要结果在随机非线性积分方程中的一个应用.In this paper,we generalize two important inequalities,and investigate the random solutions of a class of random nonlinear operator equations by means of the random fixed point index.Meanwhile,the main results generalize the famous Altman's theorem.Finally,an application to a random nonlinear integral equation is given to illustrate the usability of the obtained results.

关 键 词：随机半闭1-集压缩算子 随机不动点指数 闭凸集 实BANACH空间 Σ-代数 

分 类 号：O211.63[理学—概率论与数理统计] O177.91[理学—数学]