集值映象的KyFan变分不等式解的存在定理

设Ｘ是局部凸Ｈａｕｓｏｄｒｆｆ拓扑线空间Ｅ的非空凸子集，Ｇ：Ｘ→２＾Ｅ是连续的非空紧凸值集值映象，设ｇ：Ｘ→Ｅ是连续映身，Ｓ包含于Ｘ是非空紧凸集，Ｋ包含Ｘ是紧集，Ｐ是Ｅ上一连续半范围，若下列条件满足：（ｉ）对每－ｙ∈Ｘ／Ｋ，存在ｘ∈Ｓ，使得Ｐ（ｘ－Ｇｙ）〈Ｐｇ（ｙ）－Ｇ（ｙ）（ｉｉ）存在ｙ∈Ｘ，使得对任意Ｘ∈Ｓ有Ｐ（ｇ（ｙｂ）－Ｇｙ０）≤Ｐ（ｘ－Ｇｙｂ）Ｐ（ｇ（ｘ）－Ｇｘ）≤Ｐ（ｘ－Ｇｘ）。则存在

Existence of solutions for Ky Fan vacational inequality of set-valued maps

Irt X be a nonvid convex suest of a thualorff locally convex toPOlogical vector space E and G=X-2E a conhnuous map, with de nonvoid compact convex subSet of E for all ed X. Irt g: X-E be a continuous mapping, S=X a nonempty compact convex set, KcrX a compact set, P a continu ons sehanorm. Suppose (i) for each ye X\K there edests some re S, such that (n) a y 6 X can be found such that (iii) for each re X, Then there existS a "eX, such that Furthermore suppoSe X is a closed set and g: X--X a opening mapping, boX) is a convex set and p(g(u) -de) >0, then ne aX.