Abstract
This paper is concerned with convergence theorems and error bounds for approximate solutions of nonlinear problems, with particular applications to Urysohn integral equations. It is an abbreviated version of a more extensive projected sequel by P.M. Anselone, J. Davis and P.M. Prenter. The main goal is to clarify, simplify, and sharpen theorems and proofs on nonlinear operator approximation by Anselone [1], Atkinson [2], Moore [6,7] and Prenter [8]. More general related results have been obtained by Stummel [9, 10].
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References
Anselone, P.M., Collectively Compact Operator Approximation Theory and Applications to Integral Equations, Prentice-Hall, 1971
Atkinson, K.E., The numerical evaluation of fixed points for completely continuous operators, SIAM J. Num. Anal. 10(1973), 799–807.
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Prenter, P.M., The numerical solution of Urysohn integral equations, Report WISK 138, National Research Institute for Mathematical Sciences, Pretoria, So. Africa.
Stummel, F., Perturbations of nonlinear integral operators, to appear.
Stummel, F., Stability and discrete convergence of differentiable mappings, to appear.
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© 1976 Springer Basel AG
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Anselone, P.M. (1976). Nonlinear Operator Approximation. In: Albrecht, J., Collatz, L. (eds) Moderne Methoden der Numerischen Mathematik. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 32. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5501-3_2
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DOI: https://doi.org/10.1007/978-3-0348-5501-3_2
Publisher Name: Birkhäuser, Basel
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