What is the Jensen's Functional Equation?

Let me give you a function f that takes the set of rational numbers Q and maps it to the set of rational numbers Q. Let’s say the function f satisfy the following functional equation, where if you take any pair of rational numbers x and y, we have (f(x)+f(y))/2 is the same thing as f((x+y)/2). The game now is to determine all such functions f that satisfy this functional equation and if it happens to be no functions that satisfy this functional equation, why is there none?

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[parthosaha]

Oh yeah, I finally understood Jensen's Functional Equation. I tried to learn it before but couldn't understand it. You explained very beautifully and easily.

[maxmax]

Is there a way to to directly solve it without using the substitution?

[Ki]

Hey! How do you animate your videos? I like your style and might start posting my own videos