Abstract
Let X be a real vector space and J be a nontrivial real interval. We determine all solutions (g, M, H) of the equation $$ g(x + M(g(x))y) = H(g(x),g(y)) for x,y \in X, $$ under the assumptions that g: X → J is continuous on rays, M: J → R is continuous and H: J 2 → J is associative.
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