随机凹泛函型随机拉伸与压缩的随机不动点定理

摘要

By combining the random topological degree computation method with some known results in recent papers, a random concave functional is introduced in this paper, and a random retract in Banach space is constructed. We not only obtain two important results of the random topological degree, but also prove random expansion and compression type random fixed point theorems for a kind of random concave functionals. These theorems generalize some results in existing papers.%本文将随机拓扑度的计算方法与已有文献中结果相结合,引入了一个随机凹泛函,构造了Banach空间中的随机收缩核,得到了随机拓扑度的两个重要结果,证明了一类随机凹泛函的随机拉伸与压缩随机不动点定理.这些结果推广了已有文献中的一些结论,使得随机拓扑度能够在更广范围得到应用.