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Question Number 148990 by gsk2684 last updated on 02/Aug/21

let f:R→R be a continuius function  such that for any two real numbers  x and y ∣f(x)−f(y)∣≤10∣x−y∣^(201)   then prove that  f(2019)+f(2022)=2 f(2021)

$${let}\:{f}:{R}\rightarrow{R}\:{be}\:{a}\:{continuius}\:{function} \\ $$$${such}\:{that}\:{for}\:{any}\:{two}\:{real}\:{numbers} \\ $$$${x}\:{and}\:{y}\:\mid{f}\left({x}\right)−{f}\left({y}\right)\mid\leqslant\mathrm{10}\mid{x}−{y}\mid^{\mathrm{201}} \\ $$$${then}\:{prove}\:{that} \\ $$$${f}\left(\mathrm{2019}\right)+{f}\left(\mathrm{2022}\right)=\mathrm{2}\:{f}\left(\mathrm{2021}\right) \\ $$

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