Skip to main content
SpringerLink
Log in

Remarks on non-linear functional equations

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Browder, F. E.: The solvability of non-linear functional equations. Duke Math. J.30, 557–560 (1963).

    Google Scholar 

  2. —— Remarks on nonlinear functional equations. Proc. Nat. Acad. Sci. U.S.51, 985–989 (1964).

    Google Scholar 

  3. —— Existence and uniqueness theorems for solutions of nonlinear boundary value problems. Applications of nonlinear partial differential equations in mathematical physics. Proc. Am. Math. Soc. Symp. Appl. Math.17, 24–49 (1965).

    Google Scholar 

  4. —— Fixed-point theorems for noncompact mappings in Hilbert space. Proc. Nat. Acad. Sci. U.S.53, 1272–1276 (1965).

    Google Scholar 

  5. —— Mapping theorems for noncompact nonlinear operators in Banach spaces. Proc. Nat. Acad. Sci. U.S.54, 337–342 (1965).

    Google Scholar 

  6. Dunford, N., andJ. T. Schwartz: Linear operators, Part I. New York: Interscience 1958.

    Google Scholar 

  7. Folkman, J. H.: On functions that commute with full functions. Proc. Am. Math. Soc.17, 383–386 (1966).

    Google Scholar 

  8. Gelfand, I. M., andN. Ya. Vilenkin: Generalised functions, Vol. 4. New York: Academic Press 1964.

    Google Scholar 

  9. George, M. D.: The spectrum of an operator in Banach space. Proc. Am. Math. Soc.16, 980–982 (1965).

    Google Scholar 

  10. Göhde, D.: Zum Prinzip der kontraktiven Abbildung. Math. Nachr.30, 251–258 (1965).

    Google Scholar 

  11. Graves, L. M.: Topics in the functional calculus. Bull. Am. Math. Soc.41, 641–662 (1935).

    Google Scholar 

  12. Isbell, J. R.: Commuting mappings of trees. Bull. Am. Math. Soc.63, 419 (1957).

    Google Scholar 

  13. Krasnosel'skii, M. A.: Two comments on the method of successive approximation. Usp. Mat. Nauk10, 123–127 (1955).

    Google Scholar 

  14. —— Topological methods in the theory of nonlinear integral equations. New York: Macmillan 1964.

    Google Scholar 

  15. Lumer, G., andR. S. Phillips: Dissipative operators in a Banach space. Pacific J. Math.11, 679–698 (1961).

    Google Scholar 

  16. Petryshyn, W. V.: Remarks on fixed point theorems and their extensions (to appear).

  17. Stone, M. N.: Linear transformations in Hilbert space and their applications to analysis. Am. Math. Soc. Collq. Pub. vol.15, New York (1932).

  18. Zarantonello, E. H.: The closure of the numerical range contains the spectrum. Bull. Am. Math. Soc.70, 781–787 (1964).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Division, University of Sussex Falmer, Brighton, Sussex, England

    D. E. Edmunds

Authors
  1. D. E. Edmunds
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was partially supported by National Science Foundation Grant GP-3904.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Edmunds, D.E. Remarks on non-linear functional equations. Math. Ann. 174, 233–239 (1967). https://doi.org/10.1007/BF01360721

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01360721

Keywords

Search

Navigation