几种类型的凸性空间与逼近紧及度量投影的关系

Approximation Compactness and Convergence Properties of Metric Projections in L-kR(CL-kR;wCL-kR) Spaces

给出(L-wM)性质及X中非空子集序列{An}在av-strong Wijsman意义下收敛到X中非空子集A的概念,本质地揭示了三类凸性空间L-kR(CL-kR:wCL-kR)与逼近紧的关系,并且得到了L-kR(CL-kR:wCL-kR)空间的度量投影集序列PAn(xn)中点列{yn}∈PAn(xn),n≥1的某些收敛性结果.

（L- wM） properties and the conceptions of nonempty subset sequence {An} convergent to a nonempty subset A in the av-strong Wijsman snese are introduced in Banach spaces X. The relations between approximation compactness and L--kR（CL--kR;wCL--kR） spaces are dicussed. Meanwhile,some convergence properties of metric projections in L--kR （CL--kR;wCL-- kR） spaces are studied.