Fixed point properties, invariant means and invariant projections related to hypergroups

Let K be a hypergroup with a Haar measure. This paper consists of two themes; fixed point properties for non-expansive and affine maps. The first theme provides a condition when a non-expansive self-map on a weak (weak⁎) compact convex subset of several function spaces over K has a fixed point while the second theme presents some applications of common fixed point properties for affine actions of K.