Function satisfying a Holder condition of exponent 4/3

Let $f:[0,2]\to\mathbb R$ be such that $|f(x)-f(y)|\le|x-y|^{4/3}$ for all $x,y\in[0,2]$. If $\int_0^2f(x)\,dx=\frac23$, then $\sum_{k=1}^{2019}f\left(\frac1k\right)$ equals __________