finite dimensional euclidean space meaning in Chinese
有限维欧几里得空间
Examples
- The same rank lipschitz continuous development of single - valued mappings is proven by means of partially ordered theory on finite dimensional euclidean spaces . the problem that under what conditions the - resolvent operator of a maximal tj - monotone set - valued mapping is a lipschitz continuous single - valued mapping on whole space , which also answers the open problem mentioned above , is studied on finite dimensional euclidean spaces . the problem is researched that under what conditions the - resolvent operator of - subdifferential mapping of a proper functional is a lipschitz continuous single - valued mapping on whole space
?引入了集值映射的-预解算子概念；借助于偏序理论证明了有限维欧氏空间中的单值映射可同秩lipschitz连续拓展；讨论了有限维欧氏空间中的极大-单调集值映射的-预解算子在什么条件下是整个空间上的一个lipschitz连续的单值映射，这一结果也在有限维空间上解决了上面提到的公开问题；还讨论了真泛函的-次微分映射的-预解算子在什么条件下是整个空间上的一个lipsehitz连续的单值映射。 - The existence conditions of unique solutions are discussed by using - reslovent operators for set - valued mixed quasi - variational - like inequality and generalized set - valued variational inclusion problems on finite dimensional euclidean spaces ; respectively . the problem that under what conditions the solution set is nonempty ( not necessarily unique solution ) is
?利用-预解算子在有限维空间中探讨了集值混合拟类变分不等式问题和广义集值变分包含问题存在唯一解的条件；利用分析的方法在实hilbert空间中讨论了集值混合拟类变分不等式问题解集的非空性(不一定只有唯一解) 。 - One is , based on answering the above open problem on a finite dimensional euclidean space by means of partially ordered theory , to research the existence of solutions , global error bounds of proximal solutions and sensitivity of parametric unique solutions and present a class of variable - parameter three - step iterative algorithms for generalized set - valued variational inclusion problems by using - resolvent operator of set - valued mapping . two is to consider the convexity , closedness and boundedness of the solution set of general set - valued variational inclusion problems and the sensitivity of the parametric solution set by means of graphical convergence theory . three is to discuss directly the existence of solutions by using analytical methods for set - valued mixed quasi - variational - like inequalities and suggest a class of direct variable - parameter three - step iterative algorithms for solving generalized set - valued variational inclusions
研究分有三个方面：一是借助于偏序理论在有限维欧氏空间中解决了上述公开问题，在此基础上利用集值映射的-预解算子，研究了广义集值变分包含问题解的存在性、逼近解的全局误差界、参数唯一解的灵敏性，并提出了一类变参数三步迭代算法；二是借助于图收敛理论研究了一般集值变分包含问题解集的凸性、闭性和有界性以及参数解集的灵敏性；三是用分析的方法直接讨论了集值混合拟类变分不等式问题解的存在性并提出了一类求解广义集值变分包含问题的直接变参数三步迭代算法。