MathDB
Unique function

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September 1, 2010
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Problem Statement

Given two positive real numbers aa and bb, suppose that a mapping f:R+ā†’R+f : \mathbb R^+ \to \mathbb R^+ satisfies the functional equation f(f(x))+af(x)=b(a+b)x.f(f(x)) + af(x) = b(a + b)x. Prove that there exists a unique solution of this equation.
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