Skip to main content
SpringerLink
Log in

On random nonlinear contractions

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

Abstract

A fixed point theorem for random nonlinear contraction mappings is proven. The random nonlinear contraction principle is then used to study the existence and uniqueness of solutions for a class of random nonlinear integral equations.

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

Similar content being viewed by others

References

  1. R. F. Arens, A topology for spaces of transformations,Ann. of Math. 47 (1946), 480–495.

    Google Scholar 

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

    Google Scholar 

  3. A. T. Bharucha-Reid, Random Integral Equations, New York, Academic Press, 1972.

    Google Scholar 

  4. N. Bourbaki, General Topology, Part 2 (transl.), Reading, Mass., Addison-Wesley, 1966.

  5. D. W. Boyd andJ. S. W. Wong, On nonlinear contractions,Proc. Amer. Math. Soc. 20 (1969), 458–464.

    Google Scholar 

  6. O. Hans, Random fixed point theorems, 105–125, Trans. First Prague Conf. on Information Theory, Statist. Decision Functions, and Random Processes, 1957.

  7. E. Hille andR. S. Phillips,Functional Analysis and Semi-groups, Vol. 31, Providence: Amer. Math. Soc. Colloquium Publications, 1957.

    Google Scholar 

  8. A. C. H. Lee andW. J. Padgett, On a heavily nonlinear stochastic integral equation,Utilitas Mathematica 9 (1976), 123–138.

    Google Scholar 

  9. W. J. Padgett, On a nonlinear stochastic integral equation of the Hammerstein type,Proc. Amer. Math. Soc. 38 (1973), 625–631.

    Google Scholar 

  10. W. J. Padgett andR. L. Taylor,Laws of Large Numbers for Normed Linear Spaces and Certain Frechet Spaces, Lecture Notes in Mathematics, Vol. 360, New York, Heidelberg, Berlin: Springer-Verlag, 1973.

    Google Scholar 

  11. T. T. Soong, Random Differential Equations in Science and Engineering, New York, Academic Press, 1974.

    Google Scholar 

  12. C. P. Tsokos, On a stochastic integral equation of the Volterra type,Math. Systems Theory 3 (1969), 222–231.

    Google Scholar 

  13. C. P. Tsokos andW. J. Padgett, Random Integral Equations with Applications in Life Sciences and Engineering, New York, Academic Press, 1974.

    Google Scholar 

  14. K. Yosida, Functional Analysis, Berlin, Heidelberg, New York: Springer-Verlag, 1965.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of South Carolina, 29208, Columbia, S.C., USA

    Arthur C. H. Lee & W. J. Padgett

Authors
  1. Arthur C. H. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. J. Padgett
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

AMS(MOS) Subject Classification (1970): Primary 60H99,47H10; Secondary 60H20.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, A.C.H., Padgett, W.J. On random nonlinear contractions. Math. Systems Theory 11, 77–84 (1977). https://doi.org/10.1007/BF01768469

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01768469

Keywords

Search

Navigation