M(t)={x∈X|g(x,t)≤0}下半连续的几个定理

Some Theorems on B-l.s.c. of M(t) = {x ∈ X|g(x,t)≤0}

本文引入一类比拟凸更广泛的弧拟凸和一致严格弧拟凸函数族的定义。对度量空间X×T上的集值映射。 M(t)={x∈X|g_1(x,t)≤0,(?)i∈J={1,2,…,m}}1,(?)i∈T中g_i(·,t)是拟凸拟凹或在t。∈T是一致严格弧拟凸函数时M(t)的下半连续性(Berge意义)进行了讨论,得到和[5]中关于g_i(·,t)是凸弱解析函数时相应的结论。

In this paper, the concept of a strictly are quasiconvcx function is defined. Let g(x,t) = gt(x,t),…,gm (x,t))T is continuous on the metric space X × T and gi i∈J = {1,…m) are strictly are quasiconvcx on X × {to}. to ∈ T, then some theorems on B-l.s.c. of the mapping M(t) at to are shown.