Fixed point theorems for condensing multimaps on locally G-convex spaces

In this paper we investigate the fixed point problem for condensing multimaps on locally G-convex spaces instead of the usual locally convex topological vector spaces. We show that every condensing closed self-multimap that has Γ-convex values on a nonempty complete Γ-convex subset of a locally G-convex space has a fixed point. Some fixed point results for condensing multimaps which have lower semicontinuous (l.s.c.) cores and applications to abstract economy are also presented.