On the structure of the fixed-point set of a nonexpansive mapping in a Banach space
Ronald E. Bruck · Proceedings of the American Mathematical Society · 1976
If C C is a closed convex subset of a reflexive, strictly convex Banach space E E , and T : C → E T:C \to E is a nonexpansive mapping which has a fixed-point in the interior of C C , then there exists a nonexpansive mapping T ∗ : E → E {T^{\ast }}:E \to E whose fixed-point set in C C is the fixed-point set of T T .