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The functions $\xi(s)$ and $$f(s):=\xi\left(\frac{s-i}{2}\right) + \xi\left(\frac{i+s}{2}\right)$$ grow faster than exponentially on the positive axis, hence they do not satisfy the first bound. This follows from Stirling's approximation for $\Gamma(s)$ and the fact that $\zeta(\sigma+it)$ tends to $1$ for $\sigma\to\infty$ and $|t|<10$, say.