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Asymptotic Solutions of Equations in Banach Space

Published online by Cambridge University Press:  20 November 2018

C. A. Swanson  and
M. Schulzer
C. A. Swanson
Affiliation:
University of British Columbia
M. Schulzer
Affiliation:
University of British Columbia
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The equation Px = y in Banach spaces has aroused considerable interest, particularly in view of the various situations in applied analysis which it encompasses, and consequently it has been the topic of numerous investigations (2; 9; 10; 12). Detailed references may be found in (10). The equation is of special interest because of its interpretation as an integral equation; and in turn, many problems related to differential equations can be reformulated as integral equations (5; 7; 13).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 493 - 504
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Banach, S., Théorie des opérations linéaires, Monografje Matematyczne, I (Warsaw, 1932).Google Scholar
2. Bartle, R. G., Newton's method in Banach spaces, Proc. Amer. Math. Soc., 6 (1955), 827–831.Google Scholar
3. Borel, E., Sur quelques points de la théorie des fonctions, Thèse, Annales de l'Ecole Normale (1895).Google Scholar
4. Carleman, T. G. T., Les fonctions quasi-analytiques (Paris, 1926) chapter 5.Google Scholar
5. Coddington, E. A. and Levinson, N., Theory of ordinary differential equations (McGraw- Hill, New York, 1955).Google Scholar
6. de Bruijn, N. G., Asymptotic methods in analysis (P. Noordhoff, Groningen, Netherlands, 1958).Google Scholar
7. Duff, G. F. D., Partial differential equations (University of Toronto Press, Toronto, 1956).Google Scholar
8. Erdélyi, A., Asymptotic expansions (Dover, New York, 1956).Google Scholar
9. Kaazik, Yu. Ya. and Tamme, E. E., On a method of approximate solution of functional equations, Dokl. Akad. Nauk SSSR (N.S.), 101 (1955), 981–984 (Russian).Google Scholar
10. Kantorovich, L. V., Functional analysis and applied mathematics, Translated by C. D. Benster, National Bureau of Standards (U.C.L.A., 1952).Google Scholar
11. Kolmogoroff, A. N. and Fomin, S. V., Elements of the theory of functions and functional analysis I (Graylock, Rochester, N.Y., 1957).Google Scholar
12. McFarland, J. E., An iterative solution of the quadratic equation in Banach space, Proc. Amer. Math. Soc, 9 (1958), 824–830.Google Scholar
13. Riesz, F. and Nagy, B. Sz., Functional analysis (Frederick Ungar, New York, 1955).Google Scholar
14. van der Corput, J. G., Asymptotic expansions I, Technical report I, Contract AF-18(600)- 958 (University of California, Berkeley, 1954).Google Scholar
15. Zaanen, A. C., Linear analysis (Interscience, New York, 1953).Google Scholar
16. Zagadskii, D. M., An analogue of Newton's method for non-linear integral equations, Dokl. Akad. Nauk SSSR (N.S.), 59 (1948), 1041–1044 (Russian).Google Scholar