Relationship between the elastic forward scattering amplitudes for a particle and antiparticle at finite energies

Using the general postulates the following relationship is proved:
$$ \left|\int_{E_1}^{E_2}\ln\right|\frac{f_{+}(E')}{f_{-}(E')}\left|\frac{dE'}{E'}\right|<\pi^2, $$
where $f_{+}(E)$, $(f_{-}(E))$ is the elastic forward scattering amplitude for the particle (antiparticle). $E_1$, $E_2$ – arbitrary energies in l.s. Amplitudes $f_{\pm}(E)$ are proved to have no zeros in the complex plane of $E$.