Fixed point theorems for general classes of maps acting on topological vector spaces

We present new fixed point theorems for multivalued U _c ^k-admissible maps acting on locally convex topological vector spaces. The considered multivalued maps need not be compact. We merely assume that they are weakly compact and map weakly compact sets into relatively compact sets. Our fixed point results are obtained under Schauder, LeraySchauder and Furi-Pera type conditions. These results are useful in applications and extend earlier works.