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The Measurability of Carathéodory Set-Valued Mappings and Random Fixed Point Theorems

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References

  1. A. T. Bharucha-Reid, Random Integral Equations, Academic Press (New York, 1972).

    Google Scholar 

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

    Google Scholar 

  3. P. Brunovsky, Scorza-Dragoni's theorem for unbounded set-valued functions and its applications to control problems, Matematicky Casopis, 20 (1970), 205–213.

    Google Scholar 

  4. C. Castaing and M. P. Monteiro Marques, Sweeping processes by nonconvex closed moving sets with perturbation, C. R. Acad. Sci. Paris, 319 (1994), 127–132.

    Google Scholar 

  5. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer-Verlag (Berlin, 1977).

    Google Scholar 

  6. H. Engl, Random fixed point theorems for multivalued mappings, Pacific J. Math., 76 (1978), 351–360.

    Google Scholar 

  7. O. Hans, Reduzierende zufällige Transformationen, Czech. Math. J., 7 (1957), 154–158.

    Google Scholar 

  8. C. J. Himmelberg, Fixed points of compact multifunctions, J. Math. Anal. Appl., 38 (1972), 205–207.

    Google Scholar 

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

    Google Scholar 

  10. T. Kim, K. Prikry and N. Yannelis, Carathéodory-type selections and random fixed point theorems, J. Math. Anal. Appl., 122 (1987), 393–407.

    Google Scholar 

  11. K. Kuratowski, Topology, vol 1, Fifth ed., Academic Press (New York, 1966).

    Google Scholar 

  12. N. S. Papageorgiou, Random fixed point theorems for measurable multifunctions in Banach spaces, Proc. Amer. Math. Soc., 97 (1986), 507–514.

    Google Scholar 

  13. A. P. Robertson, On measurable selections, Proc. R. S. E. (A), 72 (1972/73), 1–7.

    Google Scholar 

  14. C. A. Rogers, Hausdorff Measures, Cambridge University Press (1970).

  15. L. E. Rybinski, Random fixed points and viable random solutions of functional differential inclusions, J. Math. Anal. Appl., 142 (1989), 53–61.

    Google Scholar 

  16. M. F. Saint-Beuve, On the existence of von Neumann-Aumann's theorem, J. Functional Analysis, 17 (1974), 112–129.

    Google Scholar 

  17. A. Spacek, Zufallige Gleichungen, Czech. Math. J., 5 (1955), 462–466.

    Google Scholar 

  18. K. K. Tan and X. Z. Yuan, On deterministic and random fixed points, Proc. Amer. Math. Soc., 119 (1993), 849–856.

    Google Scholar 

  19. K. K. Tan, E. Tarafdar and X. Z. Yuan, Random variational inequality and applications to random minimization and stochastic nonlinear boundary problems, PanAmerican Math. Journal, 4 (1994), 55–71.

    Google Scholar 

  20. D. H. Wagner, Survey of measurable selection theorems, SIAM J. Control. Optim, 15 (1977), 859–903.

    Google Scholar 

  21. W. Zygmunt, A note concerning the Scorza-Dragoni's type property of the compact multivalued multifunction, Rend. Accad. Naz. Sci. XL Mem. Mat., 13 (1989), 31–33.

    Google Scholar 

  22. W. Zygmunt, On superpositionally measurable semi-Carathéodory multifunctions, Comm. Math. Univ. Carolinae, 33 (1992), 73–77.

    Google Scholar 

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Tarafdar, E., Watson, P. & Yuan, XZ. The Measurability of Carathéodory Set-Valued Mappings and Random Fixed Point Theorems. Acta Mathematica Hungarica 74, 309–319 (1997). https://doi.org/10.1023/A:1006576304646

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