Israel Journal of Mathematics

, Volume 29, Issue 4, pp 329–345 | Cite as

Produits infinis de resolvantes

  • H. Brezis
  • P. L. Lions


This paper is concerned with the convergence of the sequence χ n =(I n A)−1χ n−1 whereA is maximal monotone and λ n >0. Various assumptions onA and λ n are considered.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. B. Baillon,Quelques propriétés de convergence asymptotique pour les contractions impaires, C. R. Acad. Sci. Paris283 (1976), 587–590.zbMATHMathSciNetGoogle Scholar
  2. 2.
    J. B. Baillon and G. Haddad,Quelques propriétés des opérateurs angle-bornés et n-cycliquement monotones, Israel J. Math.26 (1977), 137–150.zbMATHMathSciNetGoogle Scholar
  3. 3.
    H. Brezis,Opérateurs maximaux monotones, Lecture note no5, North-Holland, 1973.Google Scholar
  4. 4.
    F. Browder and W. Petryshyn,The solution by iteration of nonlinear functional equations in Banach spaces. Bull. Amer. Math. Soc.72 (1966), 571–575.zbMATHMathSciNetGoogle Scholar
  5. 5.
    R. Bruck,Asymptotic convergence of nonlinear contraction semi-groups in Hilbert space, J. Functional Analysis18 (1975), 15–26.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    R. Bruck,An interative solution of a variational inequality for certain monotone operators in Hilbert space, Bull. Amer. Math. Soc.81 (1975), 890–892, Corrigendum82 (1976).zbMATHMathSciNetGoogle Scholar
  7. 7.
    M. Crandall and A. Pazy,On the range of accretive operators, Israel J. Math.,27 (1977), 235–246.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    A. Genel and J. Lindenstrauss,An example concerning fixed points, Israel J. Math.22 (1975), 81–86.zbMATHMathSciNetGoogle Scholar
  9. 9.
    Z. Opial,Weak convergence of the successive approximations for nonexpansive mappins in Banach spaces, Bull. Amer. Math. Soc.73 (1967), 591–597.zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    R. T. R. Rockafellar,Monotone operators and the proximal point algorithm, SIAM J. Control14 (1976), 877–898.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1978

Authors and Affiliations

  • H. Brezis
    • 1
    • 2
  • P. L. Lions
    • 1
    • 2
  1. 1.Dept. de MathématiquesUniversité Paris VIParis 05France
  2. 2.E.N.S.Paris 05France

Personalised recommendations