A connection between fixed-point theorems and tiling problems

The classic Banach Contraction Principle stales that any contraction on a c omplete metric space has a unique fixed point. Rather than requiring that a single operator be a contraction, we consider a minimum involving a set of powers of that operator and derive fixed-point results. Ordinary analytica l techniques would be extremely unwieldy, and so we develop a method for at tacking this problem by considering a related problem on tiling the integer s. (C) 1999 Academic Press.