Skip to main content
Log in

Convergence of approximants to fixed points of nonexpansive nonlinear mappings in banach spaces

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliography

  1. Beurling, A., & A. E. Livingston, A theorem on duality mappings in Banach spaces. Ark. Math. 4, 405–411 (1961).

    Google Scholar 

  2. Brodski, M. S., & D. P. Milman, On the center of a convex set. Dokladi Akad. Nauk SSSR (N.S.) 59, 837–840 (1948).

    Google Scholar 

  3. Browder, F. E., Nonlinear elliptic boundary value problems. Bull. Amer. Math. Soc. 69, 862–874 (1963).

    Google Scholar 

  4. Browder, F. E., Nonlinear elliptic problems, II. Bull. Amer. Math. Soc. 70, 299–302 (1964).

    Google Scholar 

  5. Browder, F. E., Nonlinear elliptic boundary value problems, II. Trans. Amer. Math. Soc. 117, 530–550 (1965).

    Google Scholar 

  6. Browder, F. E., On a theorem of Beurling and Livingston. Canad. Jour. Math. 17, 337–342 (1965).

    Google Scholar 

  7. Browder, F. E., Multivalued monotone nonlinear mappings and duality mappings in Banach spaces. Trans. Amer. Math. Soc. 118, 338–351 (1965).

    Google Scholar 

  8. Browder, F. E., Nonlinear monotone operators and convex sets in Banach spaces. Bull. Amer. Math. Soc. 71, 783–785 (1965).

    Google Scholar 

  9. Browder, F. E., Existence and uniqueness theorems for solutions of nonlinear boundary value problems. Proc. Amer. Math. Soc. Symposia on Applied Math. 17, 24–49 (1965).

    Google Scholar 

  10. Browder, F. E., Existence of periodic solutions for nonlinear equations of evolution. Proc. Nat. Acad. Sci. U.S.A. 53, 1100–1103 (1965).

    Google Scholar 

  11. Browder, F. E., Fixed point theorems for noncompact mappings in Hubert space. Proc. Nat. Acad. Sci. U.S.A. 53, 1272–1276 (1965).

    Google Scholar 

  12. Browder, F. E., Mapping theorems for noncompact nonlinear mappings in Banach spaces. Proc. Nat. Acad. Sci. U.S.A. 54, 337–243 (1965).

    Google Scholar 

  13. Browder, F. E., Nonexpansive nonlinear operators in Banach spaces. Proc. Nat. Acad. Sci. U.S.A. 54, 1041–1044 (1965).

    Google Scholar 

  14. Browder, F. E., Fixed point theorems for nonlinear semicontractive mappings in Banach spaces. Arch. for Rational Mech. and Anal. 21, 259–269 (1966).

    Google Scholar 

  15. Browder, F. E., Problemes nonlinéaires. University of Montreal Lecutre Notes, Summer 1965.

  16. Browder, F. E., On the unification of the calculus of variations and the theory of monotone nonlinear operators in Banach spaces. Proc. Nat. Acad. Sci. U.S.A., 56, 419–425 (1966).

    Google Scholar 

  17. Browder, F. E., Existence and approximation of solutions of nonlinear variational inequalities. Proc. Nat. Acad. Sci. U.S.A., 56, 1080–1086 (1966).

    Google Scholar 

  18. Browder, F. E., Periodic solutions of nonlinear initial value problems (to appear).

  19. Browder, F. E., & D. G. de Figueiredo, J-monotone nonlinear operators in Banach spaces (to appear in Indig. Math.).

  20. Browder, F. E., & W. V. Petryshyn, The solution by iteration of linear functional equations in Banach spaces. Bull. Amer. Math. Soc. 72, 566–570 (1966).

    Google Scholar 

  21. Browder, F. E., & W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces. Bull. Amer. Math. Soc. 72, 571–575 (1966).

    Google Scholar 

  22. Edelstein, M., On nonexpansive mappings of Banach spaces. Proc. Cambridge Phil. Soc. 60, 439–447 (1964).

    Google Scholar 

  23. Hartman, P., Generalized Lyapounov functions and nonlinear functional equations. Annali di Mat. (IV) 69, 303–320 (1965).

    Google Scholar 

  24. Hartman, P., & G. Stampacchia, On some nonlinear elliptic functional differential equations. Acta Math. 115, 271–310 (1966).

    Google Scholar 

  25. Kacurovski, R. I., Monotone nonlinear operators in Banach spaces. Dokladi Akad. Nauk SSSR (N.S.) 163, 559–562 (1965).

    Google Scholar 

  26. Kirk, W. A., A fixed point theorem for mappings which do not increase distance. Amer. Math. Monthly 72, 1004–1006 (1965).

    Google Scholar 

  27. Lions, J. L., & G. Stampacchia, Inéquations variationelles noncoércives. C. R. Acad. Sci. Paris 261, 25–27 (1965).

    Google Scholar 

  28. Lions, J. L., & G. Stampacchia, Variational inequalities (to appear).

  29. Minty, G. J., On a “monotonicity” method for the solution of nonlinear equations in Banach spaces. Proc. Nat. Acad. Sci. U.S.A. 50, 1038–1041 (1963).

    Google Scholar 

  30. Stampacchia, G., Formes bilinéaires coércives sur les ensembles convexes. C. R. Acad. Sci. Paris 258, 4413–4415 (1964).

    Google Scholar 

  31. Petryshyn, W.V., Projection methods in nonlinear numerical functional analysis (to appear).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by J. Serrin

The preparation of this paper was partially supported by U. S. National Science Foundation Grant GP 3552.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Browder, F.E. Convergence of approximants to fixed points of nonexpansive nonlinear mappings in banach spaces. Arch. Rational Mech. Anal. 24, 82–90 (1967). https://doi.org/10.1007/BF00251595

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00251595

Keywords

Navigation