Random approximations and fixed point theorems

Journal of Approximation Theory

Volumn 84, Issue 2, 1996, Pages 172-187

  Yuan, Xian Zhi ^a   Luo, Xun ^b   Li, Gang ^c  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b CSIRO   (Australia)

^c TEMPLE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030078446     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1996.0014     Document Type: Article

References (38)

1. 1. R. I. AUMANN, Measurable utility and the measurable choice theorem, in "Proc. Int. Colloq. La Décision, C.N.R.S., Aix-en-Provence, 1967," pp. 15-26.
2. 2. A. T. BHARUCHA-REID, Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc. 82 (1976), 641-645.
3. 3. G. BOCSAN, A general random fixed point theorem and application to random equations, Rev. Roumaine Math. Pures et Appl. 26 (1981), 375-379.
4. 4. S. S. CHANG, Some random fixed point theorems for continuous random operators, Pacific J. Math. 105 (1983), 21-31.
5. 5. X. P. DING AND K. K. TAN, A minimax inequality with application to existence of equilibrium point and fixed point theorems, Colloquium Math. 63 (1992), 233-247.
6. 6. X. P. DING AND K. K. TAN, A set-valued generalizations of Fan's best approximation theorems, Canad. J. Math. 44 (1992), 784-796.
7. 7. H. W. ENGL, Random fixed point theorems for multivalued mappings, Pacific J. Math. 76 (1978), 351-360.
8. 8. K. FAN, Extensions of two fixed point theorems of F. E. Browder, Math. Z. 112 (1969), 234-240.
9. 9. K. FAN, Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519-537.
10. 10. C. J. HIMMELBERG, Measurable relations, Fund. Math. 87 (1975), 53-72.
11. 11. S. ITOH, Random fixed point theorem with an application to random differential equations in Banach spaces, J. Math. Anal. Appl. 67 (1979), 261-273.
12. 12. A. KUCIA AND A. NOWAK, Some results and counterexamples on random fixed points, in "Trans. 10th Prague Conference on Information Theory, Stat. Decision, Funct., and Random Processes Prague, 1986," pp. 75-82, Academia, Prague, 1988.
13. 13. S. J. LEESE, Multifunctions of Souslin type, Bull. Aust. Math. Soc. 11 (1974), 395-411.
14. 14. T. C. LIN, Approximations and fixed points for condensing non-self-maps defined on a sphere, Proc. Amer. Math. Soc. 105 (1989), 66-69.
15. 15. T. C. LIN, Random approximations and random fixed point theorems for non-self-maps, Proc. Amer. Math. Soc. 103 (1988), 1129-1135.
16. 16. T. C. LIN, Approximation theorems and fixed theorems in cones, Proc. Amer. Math. Soc. 102 (1988), 502-506.
17. 17. T. C. LIN AND C. L. YEN, Applications of the proximity map to fixed point theorems in Hilbert spaces, J. Approx. Theory 52 (1988), 141-148.
18. 18. Z. S. LIU AND S. Z. CHEN, On fixed point theorems of random set-valued maps, Kexue Tongbao (Bull. Chinese Sci.) 28 (1988), 433-435.
19. 19. N. S. PAPAGEORGIOU, Random fixed point theorems for measurable multifunctions in Banach spaces, Proc. Amer. Math. Soc. 97 (1986), 507-514.
20. 20. S. REICH, Fixed point theorems in locally convex spaces, Math. Z. 125 (1972), 17-31.
21. 21. S. REICH, A random fixed point theorem, Atti Accad. Naz. Lincei 64 (1978), 65-66.
22. 22. S. REICH, Approximate selection, best approximations, fixed points and invariant sets, J. Math. Anal. Appl. 62 (1978), 104-112.
23. 23. S. REICH, Fixed point theorems for set-valued mappings, J. Math. Anal. Appl. 69 (1979), 353-358.
24. 24. C. A. ROGERS, "Hausdorff Measures," Cambridge Univ. Press, Cambridge, 1970.
25. 25. H. L. ROYDEN, "Real Analysis," 2nd ed., New York, 1968.
26. 26. L. E. RYBINSKI, Random fixed points and viable random solutions of functional differential inclusions, J. Math. Anal. Appl. 142 (1989), 53-61.
27. 27. M. F. SAINT-BEUVE, On the existence of Von Neumann-Aumann's theorem, J. Funct. Anal. 17 (1974), 112-129.
28. 28. S. SAKS, "Theory of the Integral," Dover, New York, 1968.
29. 29. V. M. SEHGAL AND S. P. SINGH, On random approximations and fixed point theorem for set valued mappings, Proc. Amer. Math. Soc. 95 (1985), 91-94.
30. 30. V. M. SEHGAL AND C. WATERS, Some random fixed point theorems for condensing operators, Proc. Amer. Math. Soc. 90 (1984), 425-429.
31. 31. V. M. SEHGAL AND C. WATERS, Some random fixed point, Contemp. Math. 21 (1983), 215-218.
32. 32. S. P. SINGH AND B. WATSON, Proximity maps and fixed points, J. Approx. Theory 39 (1983), 72-76.
33. 33. K. K. TAN AND X. Z. YUAN, On deterministic and random fixed points, Proc. Amer. Math. Soc. 119 (1993), 849-856.
34. 34. K. K. TAN AND X. Z. YUAN, Random fixed point theorems and approximation in cone, J. Math. Anal. Appl. 185 (1994), 378-390.
35. 35. K. K. TAN, E. TARAFDAR AND X. Z. YUAN, Random variational inequality and applications to random minimization and nonlinear boundary problems, Pan Amer. Math. J. 4 (1994), 55-71.
36. 36. D. H. WAGNER, Survey of measurable selection theorems, SIAM J. Control. Optim. 15 (1977), 859-903.
37. 37. H. K. XU, Some random fixed point theorems for condensing and nonexpansive operators, Proc. Amer. Math. Soc. 110 (1990), 495-500.
38. 38. X. Z. YUAN, The KKM principle, Ky Fan minimax inequalities and fixed point theorems, Nonlinear World 2 (1995), 131-169.