  For a non-trivial transcendental semigroup, escaping set I(S) is in general
S-forward invariant and it is S-completely invariant if semigroup S is abelian.
In the contrary of this result, we investigate completely invariant escaping
set K(S) in different way even if semigroup S is not abelian and we discuss
some properties and structure of such type of escaping set. Also, we establish
some relations between completely invariant escaping set K(S) and the general
escaping set I(S).

Dynamical Systems