Acta mathematica scientia,Series A ›› 2003, Vol. 23 ›› Issue (2): 161-168.

• Articles • Previous Articles     Next Articles

On Well Posedness of Generalized Mutually Approximation Problem

 NI Ren-Xin-   

  • Online:2003-04-25 Published:2003-04-25
  • Supported by:

    基金项目:国家自然科学基金资助项目

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.

CLC Number: 

  • 41A28
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