On holomorphic mappings of a strip into itself with bounded distortion at infinity points

We study a class of holomorphic mappings of the strip, symmetric with respect to the real axis, into itself. It is supposed that mappings have bounded deviation from the identity transformation on the real axis. We have obtained distortion theorems for the class of functions and indicated univalence domains that arise when certain values of the parameter characterizing the deviation of the mapping from the identity transformation on the real axis.