Bulletin of the American Mathematical Society

The solution by iteration of nonlinear functional equations in Banach spaces

F. E. Browder and W. V. Petryshyn

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 72, Number 3 (1966), 571-575.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183527975

Mathematical Reviews number (MathSciNet)
MR0190745

Zentralblatt MATH identifier
0138.08202

Citation

Browder, F. E.; Petryshyn, W. V. The solution by iteration of nonlinear functional equations in Banach spaces. Bull. Amer. Math. Soc. 72 (1966), no. 3, 571--575. https://projecteuclid.org/euclid.bams/1183527975


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References

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  • 2. F. E. Browder, On the iteration of transformations in noncompact minimal dynamical systems, Proc. Amer. Math. Soc. 9 (1958), 773-780.
  • 3. F. E. Browder, Existence of periodic solutions for nonlinear equations of evolution, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1100-1103.
  • 4. F. E. Browder, Fixed point theorems for noncompact mappings in Hilbert Space, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1272-1276.
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  • 6. F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041-1044.
  • 7. F. E. Browder, Fixed point theorems for nonlinear semicontractive mappings in Banach spaces, Arch. Rational Mech. Anal., (to appear).
  • 8. 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.
  • 9. W. A. Kirk, A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly 72 (1965), 1004-1006.
  • 10. M. A. Krasnoselskiĭ, Two remarks about the method of successive approximations, Uspehi Mat. Nauk 10 (1955), no. 1 (63), 123-127.
  • 11. W. V. Petryshyn, On the construction of fixed points and solutions of nonlinear equations with demicompact mappings, (to appear).
  • 12. H. Schaefer, Über die Methode sukzessiver Approximationen, Jber. Deutsch. Math.-Verein. 59 (1957), 131-140.