Bulletin of the American Mathematical Society

Weak convergence of the sequence of successive approximations for nonexpansive mappings

Zdzisław Opial

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 73, Number 4 (1967), 591-597.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183528964

Mathematical Reviews number (MathSciNet)
MR0211301

Zentralblatt MATH identifier
0179.19902

Citation

Opial, Zdzisław. Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Amer. Math. Soc. 73 (1967), no. 4, 591--597. https://projecteuclid.org/euclid.bams/1183528964


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References

  • 1. F. E. Browder, Fixed-point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1272-1276.
  • 2. F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041-1044.
  • 3. F. E. Browder, Fixed point theorems for nonlinear semicontractive mappings in Banach paces, Arch. Rational Mech. Anal. 21 (1966), 259-269.
  • 4. F. E. Browder, W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 571-575.
  • 5. W. A. Kirk, A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly 72 (1965), 1004-1006.
  • 6. M. A. Krasnosel'skiĭ, Two observations about the method of successive approximations, Uspehi Mat. Nauk 10 (1955), no. 1 (63), 123-127 (Russian).
  • 7. H. Schaefer, Über die Methode sukzessiver Approximationen, Jber. Deutsch. Math.-Verein. 59 (1957), 131-140.