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5

Part of 2001 Miklós Schweitzer

Problems(1)

Miklós Schweitzer 2001 Problem 5

Source:

2/12/2017
Prove that if the function ff is defined on the set of positive real numbers, its values are real, and ff satisfies the equation f(x+y2)+f(2xyx+y)=f(x)+f(y)f\left( \frac{x+y}{2}\right) + f\left(\frac{2xy}{x+y} \right) =f(x)+f(y) for all positive x,yx,y, then 2f(xy)=f(x)+f(y)2f(\sqrt{xy})=f(x)+f(y) for every pair x,yx,y of positive numbers.
Miklos Schweitzerfunctionfunctional equationreal analysis