Some random fixed point theorems for condensing operators
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- by V. M. Sehgal and Charles Waters PDF
- Proc. Amer. Math. Soc. 90 (1984), 425-429 Request permission
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
- A. T. Bharucha-Reid, Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc. 82 (1976), no. 5, 641–657. MR 413273, DOI 10.1090/S0002-9904-1976-14091-8
- A. T. Bharucha-Reid, Random integral equations, Mathematics in Science and Engineering, Vol. 96, Academic Press, New York-London, 1972. MR 0443086
- Ward Cheney and Allen A. Goldstein, Proximity maps for convex sets, Proc. Amer. Math. Soc. 10 (1959), 448–450. MR 105008, DOI 10.1090/S0002-9939-1959-0105008-8
- Ky Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z. 112 (1969), 234–240. MR 251603, DOI 10.1007/BF01110225
- Shigeru Itoh, Random fixed-point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl. 67 (1979), no. 2, 261–273. MR 528687, DOI 10.1016/0022-247X(79)90023-4
- Arunava Mukherjea, Transformations aléatoires séparables: Théorème du point fixe aléatoire, C. R. Acad. Sci. Paris Sér. A-B 263 (1966), A393–A395 (French). MR 211456
- 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 (English, with Italian summary). MR 0383166
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 425-429
- MSC: Primary 47H10; Secondary 54H25, 60H25
- DOI: https://doi.org/10.1090/S0002-9939-1984-0728362-7
- MathSciNet review: 728362