Journal of the
Korean Mathematical Society JKMS

We give general fixed point theorems for compact multimaps in the ``better'' admissible class $\frak B^\kappa$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. %which include another known theorems in more than ten papers. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.

Keywords: the Schauder fixed point theorem, multimap (map), closed map, compact map, acyclic, admissible (in the sense of Klee), Hausdorff topological vector space (t.v.s.), $\Phi$-condensing map

MSC numbers: Primary 47H10, 54C60; Secondary 54H25, 55M20