[[abstract]]This thesis will obtain a main result by extending the Theorem of R. Smarzewski [9] in a uniformly convex in every direction (UCED) Banach space:
Let X be a UCED Banach space, and  C=∪Ck a union of nonempty weakly compact convex subsets   of X. Suppose T  is a  firmly nonexpansive mapping for some 0≦λ≦1 . Then T has a fixed point in C.

[[author]]W. S. Duh