Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Some random fixed point theorems for condensing operators

Authors: V. M. Sehgal and Charles Waters
Journal: Proc. Amer. Math. Soc. 90 (1984), 425-429
MSC: Primary 47H10; Secondary 54H25, 60H25
MathSciNet review: 728362
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we obtain several random fixed point theorems including a stochastic generalization of the classical Rothe fixed point theorem. The results herein improve a recent result of Bharucha-Reid and Mukherjea and also some similar results of Itoh.

References [Enhancements On Off] (What's this?)

  • [1] A. T. Bharucha-Reid, Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc. 82 (1976), 641-645. MR 0413273 (54:1390)
  • [2] -, Random integral equations, Academic Press, New York, 1972. MR 0443086 (56:1459)
  • [3] W. E. Cheney and A. A. Goldstein, Proximity maps for convex sets, Proc. Amer. Math. Soc. 10 (1959), 448-450. MR 0105008 (21:3755)
  • [4] Ky Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z. 112 (1969), 230-240. MR 0251603 (40:4830)
  • [5] S. Itoh, Random fixed point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl. 67 (1979), 261-273. MR 528687 (80f:60059)
  • [6] A. Mukherjea, Transformations aléatoires séparables, Théorème du point fixe aléatoire, C. R. Acad. Sci. Paris Sér. A-B 263 (1966), 393-395. MR 0211456 (35:2336)
  • [7] C. H. Su and V. M. Sehgal, Some fixed point theorems for nonexpansive mappings in locally convex spaces, Boll. Un. Mat. Ital. (4) 10 (1974), 598-601. MR 0383166 (52:4047)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H10, 54H25, 60H25

Retrieve articles in all journals with MSC: 47H10, 54H25, 60H25

Additional Information

Keywords: Measurable maps, random fixed point, condensing random operator
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society