Z-P-S空间中非线性算子方程Ax=μx的可解性

Solvability of nonlinear operator equation Ax=μxin Z-P-S Space

利用Menger概率线性赋范空间中半闭1-集压缩算子的拓扑度理论研究Z-P-S空间中非线性算子方程Ax=μx的可解性问题,所得结果推广了相关文献中的主要结果,并得到一些新的结果。最后,给出主要结果的一个具体应用。

It utilized the topological degree theory of semi-closed 1-set-contractive operators.The solvability of a class of nonlinear operator equations Ax=μxin Z-P-S spaces was studied accordingly.Our results generalized the corresponding results in some references.Some new results were obtained as well.Finally,an example was given to illustrate our main results.