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Abstract

We consider linear operator equations of the so called second kind which are of the form
$$ {\text{x}} - {\text{Kx}} = \left( {{\text{I}} - {\text{K}}} \right){\text{x}} = {\text{y}} $$
(1.1)
where K is a continuous linear operator mapping a Banach space X into itself and I:X→X denotes the identical mapping. We assume that the inverse (I-K)-1 of (I-K) exists on X and is continuous so that for each choice of y∈X the equation (1.1) has a unique solution x∈X.

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References

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    Anselone, Ph. M. : Collectively Compact Operator Approximation Theory. Prentice-Hall, Inc., Englewood Cliffs, New Jersey 1971.Google Scholar
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    Barrodale, J. and A. Young: Computational Experience in Solving Linear Operator Equations Using the Chebychev Norm. In: Numerical Approximation to Functions and Data, edited by J. G. Hayes, The Athlone Press, London 1970.Google Scholar
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    Krabs, W.: Optimierung und Approximation. Teubner-Verlag, Stuttgart 1975.Google Scholar

Copyright information

© Springer Basel AG 1979

Authors and Affiliations

  • W. Krabs

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