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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[@parthosaha4170]

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.

[@1psi3colourmath]

Great, Thanks!

[@edmundwoolliams1240]

You deserve more subs

[@1psi3colourmath]

Thanks, I hope that my channel will grow more, would appreciate if you like, share and watch more of my videos. Thanks for your support! 🙏

[@Ki0212]

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

[@1psi3colourmath]

My videos are made using manim, the software used by 3b1b, the whole animate is programmed using python

[@NaN_000]

Nice 🙂

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Thanks! Glad you like it!

[@NaN_000]

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[@rocky171986]

Are you Singaporean?

[@1psi3colourmath]

Hi there, I am actually a Malaysian.