Bulletin of the
Korean Mathematical Society BKMS

Using the notions of admissibility, local convexity and measure of noncompactness, we give new fixed point theorems for quasicompact or condensing multivalued mappings with domains that are not necessarily convex subsets of an arbitrary topological vector space.

Keywords: topological vector spaces, admissible sets, locally convex sets, starshaped sets, fixed points, quasicompact multivalued mappings, $\varphi$-measure of noncompactness, $(\gamma,\varphi)$-condensing mappings

MSC numbers: Primary 47H10, 54C60, 47H09. Secondary 52A30