关键词: 广义共同逼近问题；适定性；Minkowski泛函；有界相对弱紧集；极小化序列

Abstract:

Let C be a closed bounded convex subset of a realBanachspace 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 ofall 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 hasa uniquesolution (x0,z0) and every minimizing sequence converges strongly to (x0,z0). Under the assumption 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［1］,Li［2］,De Blasi andMyjak［3］ and other authors.

Key words: Generalized mutually approximation problem, Well posedne ss, Minkowski functional, Boundedly relatively weakly compact set, Minimizing se quence.