中文摘要：

建立了非紧完备L-凸度量空间中的GLsKKM定理．作为应用，获得了Ky Fan截口定理，极大元定理和Fan—Browder型不动点定理．

英文摘要：

In this paper, a GLsKKM theorem is established in noncompact complete L-convex metric spaces. As applications, a Ky Fan section theorem, maximal element theorem and Fan-Browder type fixed point theorem are obtained.