The exact upper bound on the decreasing function $f$ is $\sup_{x\in[0,1]} f(x)=f(0)=1$. The exact value of $\omega(f,\varepsilon)$ for $\varepsilon>0$ is $f(1-1\wedge\varepsilon)-f(1)=1\wedge\varepsilon^a$, because $f$ is deacreasing and concave.
Iosif Pinelis
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