Estimations of distortion of the modules for the mappings with $s$-averaged characteristic

In the present work geometrical properties of mappings with $s$-averaged characteristic are investigating. For such mappings the estimation theorems for distortion of the module of a family of curves and the module of an image of a family of curves are proved. The obtained results enable to establish equivalence of the geometrical and analytical definitions of the mappings with $s$-averaged characteristic and give additional mathematical methods at their research.