Fixed point theorems for nonexpansive mappings satisfying certain boundary conditions
Fixed point theorems for nonexpansive mappings satisfying certain boundary conditions
Let $K$ be a bounded closed convex subset of a Banach space $X$ with $\operatorname {int} K \ne \emptyset$, and suppose $K$ has the fixed point property with respect to nonexpansive self-mappings (i.e., mappings $U:K \to K$ such that $||U(x) - U(y)|| \leq ||x - y||,x,y \in K)$. Let $T:K …