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-預(yù)解算子概念;借助于偏序理論證明了有限維歐氏空間中的單值映射可同秩lipschitz連續(xù)拓展;討論了有限維歐氏空間中的極大-單調(diào)集值映射的-預(yù)解算子在什么條件下是整個(gè)空間上的一個(gè)lipschitz連續(xù)的單值映射,這一結(jié)果也在有限維空間上解決了上面提到的公開問題;還討論了真泛函的-次微分映射的-預(yù)解算子在什么條件下是整個(gè)空間上的一個(gè)lipsehitz連續(xù)的單值映射。
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-預(yù)解算子在有限維空間中探討了集值混合擬類變分不等式問題和廣義集值變分包含問題存在唯一解的條件;利用分析的方法在實(shí)hilbert空間中討論了集值混合擬類變分不等式問題解集的非空性(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 研究分有三個(gè)方面:一是借助于偏序理論在有限維歐氏空間中解決了上述公開問題,在此基礎(chǔ)上利用集值映射的-預(yù)解算子,研究了廣義集值變分包含問題解的存在性、逼近解的全局誤差界、參數(shù)唯一解的靈敏性,并提出了一類變參數(shù)三步迭代算法;二是借助于圖收斂理論研究了一般集值變分包含問題解集的凸性、閉性和有界性以及參數(shù)解集的靈敏性;三是用分析的方法直接討論了集值混合擬類變分不等式問題解的存在性并提出了一類求解廣義集值變分包含問題的直接變參數(shù)三步迭代算法。