Abstract
The present paper discusses the connection between fixed points in function spaces and finite dimensional approximations. Utilizing algebraic properties of the space of continuous functions C[0,1] we obtain
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(i)
a simple criterion for testing consistency of an approximation.
Theorem: Consistency is equivalent to TN(a)=a for all N and for all generators {a}={a1, a2, ..., an} of the algebra,
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(ii)
an understanding of stability from an algebraic point of view,
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(iii)
a simple proof for the equivalence theorem.
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© 1979 Springer-Verlag
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Forster, W. (1979). On numerical approximation of fixed points in C[0,1]. In: Peitgen, HO., Walther, HO. (eds) Functional Differential Equations and Approximation of Fixed Points. Lecture Notes in Mathematics, vol 730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064314
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DOI: https://doi.org/10.1007/BFb0064314
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Print ISBN: 978-3-540-09518-7
Online ISBN: 978-3-540-35129-0
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