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乘积空间中凹泛函型锥拉伸与压缩不动点定理

DOI: 10.3969/j.issn.1005-3026.2015.02.032, PP. 301-304

Keywords: 不动点,全连续算子,锥拉伸与压缩,凹泛函,乘积空间

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Abstract:

考虑赋范线性空间的乘积空间,由因子空间中的锥生成乘积空间中的锥.全连续算子定义在乘积空间中锥与两个闭球相交得到的有界闭集上,并且值域在锥中.在由锥上一类非负正齐次凹泛函表示的混合型锥拉伸与压缩条件下,利用构造性方法将其转化为Schauder型问题,证明了几个全连续算子的不动点定理.通过例子说明这里所需要的凹泛函在常用的空间及其锥上是容易构造的.

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