A-固有算子方程x=Ax+λBx的可解性

SOLVABILITY OF x=Ax+λBx WITH A AND B A-PROPER OPERATORS

在这篇文章中,得到了一个关于A-固有算子方程x=Ax+λBx在楔形上的可解性的新结果,它部分的回答了Petryshyn1981年提出的一个开问题,由这个结果还导出一个新的拉伸与压缩的不动点定理.

In this paper,a new solvability result of x=Ax+λBx with A and B A-proper operators is obtained,which partially an-swers an open problem by Petryshyn in 1981.With application of this result,new fixed point theorems of the expansion andcompression in a wedge is obtained.