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2009
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We classify, under reasonable assumptions, all differentiable functions f for which the 'secant method' [xf(y)- yf(x)]/[f(y)- f(x)] is continuous and associative. Further, we classify all differentiable functions for which the similar type of addition xf(y) + yf(x) is associative.
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Northshield, S. (2009). On two types of exotic addition. Aequationes Mathematicae, 77.
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This article has been published in Aequationes Mathematicae.