Fixed-point theory for set valued mappings between topological vector spaces having sufficiently many linear functionals

Fixed-point theorems for multivalued maps were presented on Hausdorff topological vector spaces having linear functionals. A continuation theory was presented for the maps discussed. It was found that for the maps the property of having a fixed point is invariant using homotopy. New fixed-point theorems for weakly sequentially upper semicontinuous maps were obtained using the fixed-point results.