We provide two results that unite the following two pairs of theorems respectively. Kakutani Fixed Point Theorem. Y be an upper semicontinuous multifunction with nonempty closed convex images. Then F has a fixed point . Browder Fixed Point Theorem.
X be a multifunction with nonempty convex images and fibers relatively open in X .
Then F has a fixed point. Michael Selection Theorem. Let X be a paracompact Hausdorff topological space, and let Y be a Banach space . Y be a lower semicontinuous multifunction with nonempty closed convex images. Browder Selection Theorem.