A Generalization of The Markov-Kakutani Fixed Point Theorem
  In this announcement we generalize the Markov-Kakutani fixed point theorem for abelian semi-groups of affine transformations extending it on some class of non-commutative semi-groups. As an interesting example we apply it obtaining a generalization of the invariant version of the Hahn-Banach theorem. 
Jaroslaw Wawrzycki