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Fixed Point Theorem and Nonlinear Ergodic Theorem for Nonexpansive Semigroups Without Convexity
Abstract We first prove a nonlinear ergodic theorem for nonexpansive semigroups without convexity in a Hilbert space. Further we prove a fixed point theorem for non-expansive semigroups without convexity which generalizes simultaneously fixed point theorems for left amenable semigroups and left reversible semigroups.