广义共同逼近问题的适定性  

On Well Posedness of Generalized Mutually Approximation Problem

作　　者：倪仁兴[1] 

机构地区：[1]绍兴文理学院数学系,绍兴312000

出　　处：《数学物理学报（A辑）》2003年第2期161-168,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金资助项目 ( 1 0 2 71 0 2 5 );浙江省教育厅科研项目 ( 2 0 0 1 0 1 0 5);浙江省自然科学基金资助项目 ( 1 0 2 0 0 2 )

摘　　要：设 C是实 Banach空间 X中有界闭凸子集且 0是 C的内点 ,G是 X中非空闭的有界相对弱紧子集 .记 K( X)为 X的非空紧凸子集全体并赋 H ausdorff距离 ,KG( X)为集合 {A∈ K( X) ;A∩ G=}的闭包 .称广义共同逼近问题 min C( A,G)是适定的是指它有唯一解 ( x0 ,z0 ) ,且它的每个极小化序列均强收敛到 ( x0 ,z0 ) .在 C是严格凸和 Kadec的假定下 ,证明了 {A∈K( X) ;min C( A,G)是适定的 }含有 KG( X)中稠 Gδ子集 ,这本质地推广和延拓了包括 De Blasi,Myjak andPapini[1]、Li[2 ]和 De Blasi and Myjak[3]等人在内的近期相应结果 .Let C be a closed bounded convex subset of a real Banach space X with 0 being an interior point of C. Let G be a nonempty closed, boundedly relatively weakly compact subset of X. Let K(X) denote the space of all nonempty compact convex subset of X endowed with the Hausdorff distance. Moreover, Let K G(X) denote the closure of the set {A∈K(X);A∩G=}. A generalized mutually approximation problem min C(A,G) is said to be well posed if it has a unique solution (x 0,z 0) and every minimizing sequence converges strongly to (x 0,z 0)on that C is strictly convex and (sequentially) Kadec, that the set {A∈K G(X); min C(A,G) is well posed} contains a dense G δ subset of K G(X) is proved. The results generalize and extend the recent corresponding results due to De Blasi, Myjak and Papini ,Li ,De Blasi and Myjak and other authors.

关 键 词：广义共同逼近问题 适定性 BANACH空间 MINKOWSKI泛函 弱紧集 极小化序列 

分 类 号：O177.2[理学—数学] O174.41[理学—基础数学]