Applied Mathematics and Mechanics

, Volume 7, Issue 12, pp 1175–1188 | Cite as

Random directional contractors and their applications

  • Ding Xie-ping
Article
  • 16 Downloads

Abstract

In this paper, as the generalizations of Altman's directional contractors[4,5] and Lee and Padgett's random contractors[1,2] we introduce the concept of random directional contractors for set-valued random operators. Using the new concept and transfinite induction, we show several existence theorems to solutions of nonlinear set-valued random operator equations. Our theorems improve and generalize the corresponding results in [1,2,4,5,11]. Next, some applications of our results to nonlinear random integral and differential equations are given.

Keywords

Differential Equation Mathematical Modeling Industrial Mathematic Operator Equation Existence Theorem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Lee, A.C.H. and W.J. Padgett, Random contractors and the solution of random nonlinear equation.Nonlinear Anal. TMA,1 (1977), 175–185.Google Scholar
  2. [2]
    Lee, A.C.H. and W.J. Padgett, Random Contractors with random nonlinear majorant functions.Nonlinear Anal. TMA,3 (1979), 707–715.Google Scholar
  3. [3]
    Lee, A.C.H. and W.J. Padgett, Solution of random operator equations by random stepcontractors.Nonlinear Anal. TMA,4 (1980), 145–151.Google Scholar
  4. [4]
    Altman, M., Contractor directions, directional contractors and directional contractions for solving equations,Pacific J. Math.,62 (1976), 1–18.Google Scholar
  5. [5]
    Altman, M.,Contractors and Contractors Directions — Theory and Applications, Maroel Dekker (1977).Google Scholar
  6. [6]
    Bharucha-Reid, A.T.,Random Integral Equations, Acad. Press, New York (1974).Google Scholar
  7. [7]
    Tsokos, C.P. and W.J. Padgett,Random Integral Equations with Applications in Life Sciences and Engineering, Acad Press, New York (1974).Google Scholar
  8. [8]
    Ding Xie-ping, Existence, uniqueness and approximation of solutions for a system of nonlinear random operator equations,Nonlinear Anal. TMA,8, 6 (1984), 563–576.Google Scholar
  9. [9]
    Ding Xie-ping, Fixed point theorems of random set-valued mappings and their applications,Appl. Math. and Mech., 5, 4 (1984), 561–575.Google Scholar
  10. [10]
    Castaing, C. and M. Valadier,convex Analysis and Measurable Multi functions, Springer-Verlag (1977), 580.Google Scholar
  11. [11]
    Itoh, S., A random fixed point theorem for a multivalued contraction mapping.Pacific J. Math.,68 (1977), 85–90.Google Scholar
  12. [12]
    Ding Xie-ping, Random contractors and solutions of random operator equations,Acta Math. Sinica,29, 1 (1986), 135–144. (in Chinese)Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1986

Authors and Affiliations

  • Ding Xie-ping
    • 1
  1. 1.Sichian Normal UniversityChengdu

Personalised recommendations