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Ansorge, R.: Problemorientierte Hierarchie von Konvergenzbegriffen bei der numerischen Lösung von Anfangswertaufgaben. Math. Z. 112, 13–22 (1969).
— und Hass, R.: Konvergenz von Differenzenverfahren für lineare und nichtlineare Anfangswertaufgaben. Lecture Notes in Mathematics 159. Berlin-Heidelberg-New York: Springer 1970.
Aubin, J.P.: Approximation des espaces de distribution et des opérateurs différentiels. Bull. Soc. Math. France Mém. 12, 1–139 (1967).
— Approximation of elliptic boundary-value problems. New York: Wiley 1972.
Browder, F.E.: Approximation-solvability of nonlinear functional equations in normed linear spaces. Arch. Rat. Mech. Anal. 26, 33–42 (1967).
Dieudonné, J.: Fundations of modern analysis. New York-London: Academic Press 1960.
Grigorieff, R.D.: Zur Theorie linearer approximationsregulärer Operatoren. I und II. To appear in Math. Nachr.
Henrici, P.: Discrete variable methods in ordinary differential equations. New York-London: Wiley 1962.
— Error propagation for difference methods. New York-London: Wiley 1963.
Krasnosel'skii, M.A., Vainikko, G.M., et al.: Approximate solution of operator equations. Groningen: Wolters-Noordhoff 1972.
Lax, P.D., and Richtmyer, R.D.: Survey of the stability of linear finite difference equations. Comm. Pure Appl. Math. 9, 267–293 (1956).
Pereyra, V.: Iterated deferred corrections for nonlinear operator equations. Numer. Math. 10, 316–323 (1967).
Petryshyn, W.V.: Projection methods in nonlinear numerical functional analysis. J. Math. Mech. 17, 353–372 (1967).
— On the approximation-solvability of nonlinear equations. Math. Ann. 177, 156–164 (1968).
Reinhardt, J.: Diskrete Konvergenz nichtlinearer Operatoren in metrischen Räumen. Frankfurt: Diplomarbeit 1971.
Rinow, W.: Die innere Geometrie der metrischen Räume. Berlin-Göttingen-Heidelberg: Springer 1961.
Spijker, M.N.: On the structure of error estimates for finite-difference methods. Numer. Math. 18, 73–100 (1971).
— Equivalence theorems for non-linear finite difference methods. Numerische Lösung nichtlinearer partieller Differential-und Integrodifferentialgleichungen. Lecture Notes in Mathematics 267, 233–264. Berlin-Heidelberg-New York: Springer 1972.
Stetter, H.J.: Stability of nonlinear discretization algorithms. In J.H. Bramble (Ed.): Numerical solution of partial differential equations, 111–123. New York: Academic Press 1966.
Stummel, F.: Diskrete Konvergenz linearer Operatoren. I. Math. Ann. 190, 45–92 (1970). II. Math. Z. 120, 231–264 (1971). III. To appear, Proc. Oberwolfach Conference on Linear Operators and Approximation 1971. Int. Series of Numerical Mathematics, Vol. 20. Basel: Birkhäuser.
— Discrete convergence of mappings. To appear, Proc. Conference on Numerical Analysis, Dublin, August 1972. New York-London: Academic Press 1973.
— Discrete convergence of differentiable mappings. To appear.
Vainikko, G.M.: Galerkin's perturbation method and the general theory of approximate methods for non-linear equations. USSR Comput. Math. and Math. Phys. 7, 1–41 (1967).
Watt, J.M.: Consistency, convergence and stability of general discretizations of the initial value problem. Numer. Math. 12, 11–22 (1968).
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Stummel, F., Reinhardt, J. (1973). Discrete convergence of continuous mappings in metric spaces. In: Ansorge, R., Törnig, W. (eds) Numerische, insbesondere approximationstheoretische Behandlung von Funktionalgleichungen. Lecture Notes in Mathematics, vol 333. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060700
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DOI: https://doi.org/10.1007/BFb0060700
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