| We prove weak and strong mean ergodic theorems for weakly almost periodic functions (in the sense of Eberlein) which are defined on an abstract semigroup and take values in a Banach space. Using these results, we obtain weak and strong mean ergodic theorems for noncommutative semigroups of nonexpansive mappings, affine nonexpansive mappings and linear bounded operators in Banach spaces. These results are used to obtain new and well-known mean ergodic theorems in cases of discrete and one-parameter semigroups of linear and nonlinear mappings in Banach spaces. |
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