In this paper, we obtain explicit rates of asymptotic regularity for ergodic averages under various circumstances, and apply them to extract explicit rates of metastability for the convergence of Cesàro means. Moreover, by obtaining a rate of asymptotic regularity for an averaged Mann type iteration, we extract an effective rate of convergence depending on a modulus of regularity, and a rate of metastability by computing a modulus of uniform Fejér monotonicity. In the presence of a modulus of uniqueness, we compute a rate of metastability for averaged Mann type iterations without any condition on the coefficients. Our approach in this paper proposes a procedure that unifies methods for developing nonlinear ergodic theorems and facilitating further research.
