关于膨胀算子的几个不动点定理

不动点理论是泛函分析的重要研究课题之一，在微分方程、非线性分析、数理经济学等等学科中都有许多重要应用，而压缩算子的不动点理论则是不动点理论的基础。为此，Ｒ．Ｈ．Ｒｈｏａｄｅｓ提出了若干类型的压缩算子。本文针对Ｒ．Ｈ．Ｒｈｏａｄｅｓ的压缩算子，讨论膨胀算子的不动点问题，在王尚志等人工作的基础上提出了３种类型的膨胀算子，证明了它们的不动点定理，并给出了相应的不动点集结构。另外，还对连续算子的不动点问题

Fixed Point Theorems On Expanded Operators

This paper is designed to study the fixed point problem on expanded mappings. Three kinds of expanded mappings corresponding to the constrictive ones presented by R. H. Rhoades are presented. Also, the fixed point theorems are obtained for these mappings. Moreover, it is shown that the set of fixed points of these expanded mappings is closed. Furthermore, the fixed point problem of continuous mappings is also discussed in this paper.