  In the second part of this work was developed a technique of balayage of
finite genus $q=0,1,2,\dots$ for measures (charges) and ($\delta$-) subharmonic
functions of finite order to an arbitrary closed system of rays $S$ with vertex
at origin on the complex plane $\mathbb C$. In this third part of our work, we
use only the case $q=1$ when $S$ is a pair of oppositely directed rays, i.e.,
$S$ is a straight line as the point set, and balayage is made from both sides
of this line. We consider measures and subharmonic functions of finite type of
order $1$. This bilateral balayage of genus $1$ will be applied to the
non-triviality of weight classes of entire functions of exponential type $E$
that allocated only constraint on their growth along the line; for the full
description of subsequences of zeros for classes $E$; the existence of entire
functions-multipliers of $h$ for entire functions of exponential type $g$,
limiting by the multiplication of their growth as $fh\in E$; the possibility of
the representation of meromorphic functions in the form of a ratio of functions
from $E$. The origins of the study lies in the classical Malliavin-Rubel
Theorem on the conditions of existence of an entire function of exponential
type vanishing on a given sequence of positive numbers. These studies also are
parallel to the famous Beurling-Malliavin Theorems on the multiplier and on the
radius of completeness.
