概率收缩偶与概率赋范空间中非线性算子方程的解

PAIRED PROBABILITY CONTRACTORS AND THE SOLUTIONS OF NONLINEAR OPERATOR EQUATIONS IN PROBABILISTIC NORMED SPAE

作为概率收缩的推广,本文引入概率收缩偶的概念。借助于这一概念,讨论了概率赋范空间中一类非线性算子方程的公共解的存在性,同时建立概率收缩偶与概率压缩原理的联系,推广[1-4]的主要结果。

As a generalization of probability contractors,paired probability contractors are introduced.By virtue of this concept,the existence of common solutions of nonlinear operator equations in probabilistic normed space is obtained.The relation between paired probability contractors and probabilistic contractions is showed.The main results in[1-4]are generalized.