The use of the contraction mapping theorem with derivatives in a Banach space
Author:
J. M. Holtzman
Journal:
Quart. Appl. Math. 26 (1968), 462-465
MSC:
Primary 47.85; Secondary 34.00
DOI:
https://doi.org/10.1090/qam/233246
MathSciNet review:
233246
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Additional Information
- L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Co., New York, 1964. Translated from the Russian by D. E. Brown; Edited by A. P. Robertson. MR 0213845
- L. A. Liusternik and V. J. Sobolev, Elements of functional analysis, Russian Monographs and Texts on Advanced Mathematics and Physics, Vol. 5, Hindustan Publishing Corp., Delhi; Gordon and Breach Publishers, Inc., New York, 1961. MR 0141967
- J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, Inc., New York, N.Y., 1950. MR 0034932
- A. Halanay, Differential equations: Stability, oscillations, time lags, Academic Press, New York-London, 1966. MR 0216103
- N. W. McLachlan, Ordinary non-linear differential equations in engineering and physical sciences. 2nd ed, Oxford University Press, New York, 1956. MR 0093612
- Jack M. Holtzman, CONTRACTION MAPS AND EQUIVALENT LINEARIZATION, ProQuest LLC, Ann Arbor, MI, 1967. Thesis (Ph.D.)–Polytechnic University. MR 2616415
L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, (translation), Pergamon Press, Oxford, England, 1964
L. Liusternik and V. Sobolev, Elements of functional analysis, (translation), Ungar, New York, 1961
J. J. Stoker, Nonlinear vibrations in mechanical and electric alsystems, Interscience, New York, 1950
A. Halanay, Differential equations, Academic Press, New York, 1966
N. W. McLachlan, Ordinary non-linear differential equations in engineering and physical sciences, 2nd Ed., Oxford at the Clarendon Press, 1956
J. M. Holtzman, Contraction maps and equivalent linearization, Bell System Technical Journal (to appear, December 1967)
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Article copyright:
© Copyright 1968
American Mathematical Society
