利用Petryshyn W V(1972)中所定义的1-集压缩映象拓扑度的一些基本性质以及半闭1-集压缩映象的诸多性质讨论Banach空间中一类算子的固有值与固有元的存在性问题。当算子满足一些较弱的条件时,可以保证至少存在一个大于1的固有值以及在...利用Petryshyn W V(1972)中所定义的1-集压缩映象拓扑度的一些基本性质以及半闭1-集压缩映象的诸多性质讨论Banach空间中一类算子的固有值与固有元的存在性问题。当算子满足一些较弱的条件时,可以保证至少存在一个大于1的固有值以及在其定义域的边界上存在对应的固有元。这些结论可以用来帮助探讨非线性算子方程或方程组的解的存在性问题以及解的具体形式问题。展开更多
In 1969, Ky Fan^[3] proved that for any continuous function f from a compact convex subset M of a normed linear space X into X, there exists x E M such that ｜｜f（x） - x｜｜ = dist（f（x）,M）. Since then, there hav...In 1969, Ky Fan^[3] proved that for any continuous function f from a compact convex subset M of a normed linear space X into X, there exists x E M such that ｜｜f（x） - x｜｜ = dist（f（x）,M）. Since then, there have appeared several generalizations, extensions and applications of this result. This paper also deals with some extensions and generalizations of this result when the underlying spaces are convex metric spaces.展开更多
文摘利用Petryshyn W V(1972)中所定义的1-集压缩映象拓扑度的一些基本性质以及半闭1-集压缩映象的诸多性质讨论Banach空间中一类算子的固有值与固有元的存在性问题。当算子满足一些较弱的条件时,可以保证至少存在一个大于1的固有值以及在其定义域的边界上存在对应的固有元。这些结论可以用来帮助探讨非线性算子方程或方程组的解的存在性问题以及解的具体形式问题。
基金Supported by University Grants Commission, India(F. 30-238/2004(SR))
文摘In 1969, Ky Fan^[3] proved that for any continuous function f from a compact convex subset M of a normed linear space X into X, there exists x E M such that ｜｜f（x） - x｜｜ = dist（f（x）,M）. Since then, there have appeared several generalizations, extensions and applications of this result. This paper also deals with some extensions and generalizations of this result when the underlying spaces are convex metric spaces.
