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A Connection between Fixed-Point Theorems and Tiling Problems

✍ Scribed by Jacek R. Jachymski; Bernd Schroder; James D. Stein Jr.

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
121 KB
Volume
87
Category
Article
ISSN
0097-3165

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✦ Synopsis

The classic Banach Contraction Principle states that any contraction on a complete 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 analytical techniques would be extremely unwieldy, and so we develop a method for attacking this problem by considering a related problem on tiling the integers.

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