ERGODIC RETRACTIONS AND NONLINEAR ERGODIC THEOREMS

In this paper, we study nonlinear ergodic properties for an amenable semigroup of mappings of type (y) in a Banach space. We prove that if S is an amenable semigroup and φ= {Tt; tЄS} is a semigroup of mappings of type (y) on a weakly compact, convex subset C of a Banach space such that D(coF1/n (Tt), F(Tt)) → 0, as n → ∞ for each tЄS, then F(φ) of common fixed points of φ is nonempty and there exists a nonexpansive retraction P form C onto F(φ), such that PTt= TtP= P for each tЄS, and Px Є co {Ttx; tЄS} ??? ЄS.

Keywords:

Amenable semigroup , common fixed point , mappings of type (y) , nonexpansive mapping , nonlinear ergodic theorem , retraction