A conditional dilatation equation |
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Authors: | Walter Benz |
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Affiliation: | (1) Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, D-W-2000 Hamburg 13, Germany |
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Abstract: | Summary The following theorem holds true.Theorem.Let X be a normed real vector space of dimension 3 and let k > 0 be a fixed real number. Suppose that f: X X and g: X × X are functions satisfying x – y = k f(x) – f(y) = g(x, y)(x – y) for all x, y X. Then there exist elements and t X such that f(x) = x + t for all x X and such that g(x, y) = for all x, y X with x – y = k. |
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Keywords: | Primary 39B40, 39B70 Secondary 51A10 |
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