Skip to main content
SpringerLink
Log in

Nonlinear random equations with monotone operators in Banach spaces

  • 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. Bhurucha-Reid, A.T.: On random solutions of integral equations in Banach spaces. In: Trans. 2nd Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, pp. 27–48. Prague: Czechoslovak Acad. Sci. 1960

    Google Scholar 

  2. Bharucha-Reid, A.T.: On the theory of random equations. In: Proc. Symposia in Appl. Math.16, 40–69. Providence: Amer. Math. Soc. 1964

    Google Scholar 

  3. Bharucha-Reid, A.T.: Random integral equations. New York, London: Academic Press 1972

    Google Scholar 

  4. Bharucha-Reid, A.T.: Fixed point theorems in probabilistic analysis. Bull. Amer. Math. Soc.82, 641–657 (1976)

    Google Scholar 

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

    Google Scholar 

  6. Browder, F.E.: Non-linear equations of evolution. Ann. Math.80, 485–523 (1964)

    Google Scholar 

  7. Browder, F.E.: Remarks on nonlinear functional equations. Proc. Nat. Acad. Sci. USA51, 985–989 (1964)

    Google Scholar 

  8. Browder, F.E.: Remarks on nonlinear functional equations. II. Illinois J. Math.9, 608–616 (1965)

    Google Scholar 

  9. Browder, F.E.: Further remarks on nonlinear functional equations. Illinois J. Math.10, 275–286 (1966)

    Google Scholar 

  10. Browder, F.E.: Mapping theorems for noncompact nonlinear operators in Banach spaces. Proc. Nat. Acad. Sci. USA54, 337–342 (1965)

    Google Scholar 

  11. Browder, F.E.: Problèmes non linéaires. Montréal: Les Presses de L'Université de Montréal 1966

    Google Scholar 

  12. Dolph, C.L., Minty, G.J.: On nonlinear integral equations of the Hammerstein type. In: Nonlinear integral equations (Anselone, P.M., ed.), pp. 99–154. Madison, Wisc.: University of Wisconsin Press 1964

    Google Scholar 

  13. Dunford, N., Schwartz, J.T.: Linear operators. I. General theory. New York: Interscience 1958

    Google Scholar 

  14. Edwards, R.E.: Functional analysis, theory, and applications. New York, London: Holt 1965

    Google Scholar 

  15. Hanš, O.: Reduzierende zufällige Transformationen. Czechoslovak Math. J.7, 154–158 (1957)

    Google Scholar 

  16. Hanš, O.: Random fixed point theorems. In: Trans. First Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, pp. 43–60. Prague: Czechoslovak Acad. Sci. 1957

    Google Scholar 

  17. Hanš, O.: Generalized random variables. In: Trans. First Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, pp. 61–103. Prague: Czechoslovak Acad. Sci. 1957

    Google Scholar 

  18. Hanš, O.: Inverse and adjoint transforms of linear bounded random transforms. In: Trans. First Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, pp. 127–133. Prague: Czechoslovak Acad. Sci. 1957

    Google Scholar 

  19. Hanš, O.: Random operator equations. In: Proc. 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. II, Part I, pp. 185–202. Berkeley: University of California Press 1961

    Google Scholar 

  20. Hille, E., Phillips, R.S.: Functional analysis and semigroups. Providence: Amer. Math. Soc. 1957

    Google Scholar 

  21. Himmelberg, C.J.: Measurable relations. Fund. Math.87, 53–72 (1975)

    Google Scholar 

  22. Itoh, S.: A random fixed point theorem for a multivalued contraction mapping. Pacific J. Math.68, 85–90 (1977)

    Google Scholar 

  23. Itoh, S.: Random fixed point theorems with an application to random differential equations in Banach spaces. To appear in J. Math. Anal. Appl.

  24. Kachurovskii, R.I.: Non-linear monotone operators in Banach spaces. Uspehi Mat. Nauk23=Russian Math. Surveys23, 117–165 (1968)

    Google Scholar 

  25. Kannan, R., Salehi, H.: Random nonlinear equations and monotonic nonlinearities. J. Math. Anal. Appl.57, 234–256 (1977)

    Google Scholar 

  26. Kato, T.: Demicontinuity, hemicontinuity, and monotonicity. Bull. Amer. Math. Soc.70, 548–550 (1964)

    Google Scholar 

  27. Kato, T.: Demicontinuity, hemicontinuity, and monotonicity. II. Bull. Amer. Math. Soc.73, 886–889 (1967)

    Google Scholar 

  28. Kuratowski, K., Ryll-Nardzeski, C.: A general theorem on selectors. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.13, 397–403 (1965)

    Google Scholar 

  29. Leray, J., Lions, J.-J.: Quelques résultats de Visik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder. Bull. Soc. Math. France93, 97–107 (1965)

    Google Scholar 

  30. Minty, G.J.: On a “monotonicity” method for the solution of nonlinear equations in Banach spaces. Proc. Nat. Acad. Sci. USA50, 1038–1041 (1963)

    Google Scholar 

  31. Nashed, M.Z., Salehi, H.: Measurability of generalized inverses of random linear operators. SIAM J. Appl. Math.25, 681–692 (1973)

    Google Scholar 

  32. Prakasa Rao, B.L.S.: Stochastic integral equations of mixed type. II. J. Mathematical and Physical Sci.7, 245–260 (1973)

    Google Scholar 

  33. Špaček, A.: Zufällige Gleichungen. Czechoslovak Math. J.5, 462–466 (1955)

    Google Scholar 

  34. Troyanski, S.L.: On locally uniformly convex and differetiable norms in certain non-separable Banach spaces. Studia Math.37, 173–180 (1971)

    Google Scholar 

  35. Vainberg, A.M.: Nonlinear equations with monotone operators. Dokl. Akad. Nauk. SSSR 188=Soviet Math. Dokl.10, 1136–1138 (1969)

    Google Scholar 

  36. Vainberg, M.M.: Variational method and method of monotone operators in the theory of nonlinear equations. (Engl. transl.). New York, Toronto: Wiley 1973

    Google Scholar 

  37. Webb, J.R.L.: Mapping and fixed-point theorems for nonlinear operators in Banach spaces. Proc. London Math. Soc.20, 451–468 (1970)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-Ku, 152, Tokyo, Japan

    Shigeru Itoh

Authors
  1. Shigeru Itoh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Itoh, S. Nonlinear random equations with monotone operators in Banach spaces. Math. Ann. 236, 133–146 (1978). https://doi.org/10.1007/BF01351387

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01351387

Keywords

Search

Navigation