设C是实Banach空间X中有界闭凸子集且0是C的内点,PC(·)是关于C的Minkowski泛函.设K是Banach空间X中非空闭的有界相对弱紧子集.对X中的点x,称最大化问题maxC(x,K)为适定的是指存在唯一的(z)∈K使得pC((z)-x)=uC(x,K)和每一满足limnn→∞pC(zn-x)=uC(x,K)的序列{zn}(∈)K均强收敛到(z),其中uC(x,K)=supz∈KpC(z-x).在C是严格凸和Kadec的假定下,证得了使得最大化问题maxC(x,k)为适定的所有x∈X的全体组成的集合X0(K)是X中的剩余集.进一步,如果关于Pc(·)的凸性模是严格正的,K是X中闭的有界子集,证明了集XX0(K)是X中的σ-多孔集.这些本质地推广和延拓了包括De Blasi等,Fitzpatrick,Panda和Kapoor,Li和作者等人结果在内的近期相应结果.%Let C be a closed bounded convex subset of X with 0 being an interior point of C and pC(·) be the Minkowski functional with respect to C. Let K be a nonempty closed, boundedly relatively weakly compact subset of a Banach space X .Under the assumption that C is both strictly convex and Kadec, we prove that the set X0(K) of all x∈X such that the maximization problem maxC(x,K) is well posed is a residual subset of X .Moreover,if the modulus of convexity with respect to pC(·) is strictly positive, we show that the set XX0(K) is σ- porous in X provided that K is a nonempty closed bounded subset of X.These extend some recent results due to De Blasi et.al., Fitzpatrick, Panda and Kapoor, Li. and Ni, etc.
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