概率度量空间中的Ekeland变分原理与集值映象的Caristi重合定理<sup>*</sup>

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概率度量空间中的Ekeland变分原理与集值映象的Caristi重合定理^*

基金项目: *国家自然科学基金资助课题

摘要: 借助偏序方法,本文得到概率度量空间中之一推广形式的Ekeland变分原理及一集值形式的Caristi重合定理,同时证明了这两个定理之间的等价性.本文结果是[1,2,5,6,7,9]中相应结果的改进和推广.
- 概率度量空间 /
- Caristi重合定理 /
- Ekeland变分原理 /
- 偏序集
Abstract: By using the partial ordering method,a more general type,of Ekeland's variational principle and a set-valued Caristi's coincidence theorem in probabilistic metric spaces are obtained.In addition,we give a simple direct proof of the equivalence between these two theorems in probabilistic metric spaces.
- probabilistic metric space /
- Caristi’s coincidence theorem /
- Ekeland’s variational principle /
- partial ordering set

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