Abstract
Let X and Y be real Banach spaces, D a bounded open subset of X, D its closure in X, bdry(D) its boundary in X. We show below that for the general class of A-proper mappings, (studied by F. E. BROWDER and W. V. PETRY-SHYN in [1], [2] etc.) using the generalized degree for such mappings (introduced by F. E. BROWDER and W. V. PETRYSHYN in [1]), with respect to the given approximation scheme, the Galerkin’s perturbation method converges.
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References
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Schiop, A.I. (1972). On the Convergence of Galerkin’s Perturbation Method. In: Collatz, L., Meinardus, G. (eds) Numerische Methoden der Approximationstheorie. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 16. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5952-3_15
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DOI: https://doi.org/10.1007/978-3-0348-5952-3_15
Publisher Name: Birkhäuser, Basel
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