一组新的不动点定理

A GROUP OF NEW FIXED POINT THEOREMS

本文引进了映射的范数的概念,并利用它改进了的方法,放宽了不动点定理的条件,使之不仅适用于压缩映射与紧映射的和映射,而且也适用于下述三种映射与紧映射的和映射:收缩且一致局部压缩的映射、扩张映射、准扩张且一致局部扩张的映射。另外,我们还得一个一致局部扩张映射不动点定理与一个准扩张映射不动点定理。

In this paper,the conception of norm of mapping is imported. Make use of the conception; we improve method, soften the terms of fixed point theorem and make the theorem applies not only to sum mapping of compect mapping and condensation m-apping but also to sum mapping of compact mapping and following three kinds of mapping: contraction and uniform partial condensation mapping, extension mapping, quasi-extension and uniform partial extension mapping. Moreover, we also get a fixed point theorem of uniform partial extension mapping and a fixed point theorem of quasi-extension mapping.