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Iterative solution of linear equations in Banach spaces


Authors: J. Wayne Pace and W. G. Dotson
Journal: Proc. Amer. Math. Soc. 60 (1976), 149-156
MSC: Primary 47A50; Secondary 65J05
DOI: https://doi.org/10.1090/S0002-9939-1976-0423103-0
MathSciNet review: 0423103
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Abstract: Several results are obtained which generalize recent results of Kwon and Redheffer concerning the solution of $ u - Tu = f$ by means of iteration.


References [Enhancements On Off] (What's this?)

  • [1] F. E. Browder and W. V. Petryshyn, The solution by iteration of linear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 566-570. MR 32 #8155a. MR 0190744 (32:8155a)
  • [2] D. G. deFigueiredo and L. A. Karlovitz, On the approximate solution of linear functional equations in Banach spaces, J. Math. Anal. Appl. 24 (1968). 654-664. MR 38 #6415. MR 0238139 (38:6415)
  • [3] C. Goffman and G. Pedrick, First course in functional analysis, Prentice-Hall, Englewood Cliffs, N. J., 1965. MR 32 # 1540. MR 0184064 (32:1540)
  • [4] Y. K. Kwon and R. M. Redheffer, Remarks on linear equations in Banach space, Arch. Rational Mech. Anal. 32 (1969), 247-254, MR 40 #6284. MR 0253069 (40:6284)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0423103-0
Keywords: Iteration, linear equations
Article copyright: © Copyright 1976 American Mathematical Society

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