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References
P. L.Butzer and H.Berens, Semi-Groups of Operators and Approximation. Berlin-Heidelberg-New York 1967.
P. L. Butzer andW. Dickmeis, Direct and inverse mean ergodic theorems with rates for semigroup operators. In: Approximation and Function Spaces (Proc. Conf. Gdansk (Poland), 1979), North-Holland, 191–206, Amsterdam 1981.
P. L. Butzer andW. Dickmeis, On the sharpness of non-optimal approximation for semigroup operators. Manuscripta Math.51, 243–251 (1985).
O. V. Davydov, Some condensation theorem for semigroup operators. Manuscripta Math.79, 435–446 (1993).
C. Lizama, On an extension of the Trotter-Kato theorem for resolvent families of operators. J. Integral Equation Appl.2(2), 269–280 (1990).
C.Lizama, On Volterra equations associated with a linear operator. Proc. Amer. Math. Soc. (to appear).
C. Lizama, A mean ergodic theorem for resolvent operators. Semigroup Forum47, 227–230 (1993).
J.Prüess, Evolutionary Integral equations and Application. Monographs in Math.,87, Basel 1993.
S.-Y.Shaw, Strong and uniform ergodic theorems with rates for cosine operator functions. Research Report NSC 76-0208-M008-22, National Science Council of R.O.C., 1988.
S.-Y. Shaw, Mean ergodic theorems and linear functional equations. J. Funct. Anal.87, 428–441 (1989).
S.-Y. Shaw, Convergence rates of ergodic limits and approximate solutions. J. Approx. Theory75, 157–166 (1993).
A. E.Taylor and D. C.Lay, Introduction to Functional Analysis. 2nd. ed., New York 1980.
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Chang, JC., Shaw, SY. Rates of approximation and ergodic limits of resolvent families. Arch. Math 66, 320–330 (1996). https://doi.org/10.1007/BF01207833
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DOI: https://doi.org/10.1007/BF01207833