| Title:
             | 
Characterizations of random approximations (English) | 
| Author:
             | 
Khan, Abdul Rahim | 
| Author:
             | 
Hussain, Nawab | 
| Language:
             | 
English | 
| Journal:
             | 
Archivum Mathematicum | 
| ISSN:
             | 
0044-8753 (print) | 
| ISSN:
             | 
1212-5059 (online) | 
| Volume:
             | 
39 | 
| Issue:
             | 
4 | 
| Year:
             | 
2003 | 
| Pages:
             | 
271-275 | 
| Summary lang:
             | 
English | 
| . | 
| Category:
             | 
math | 
| . | 
| Summary:
             | 
Some characterizations of random approximations are obtained in a locally convex space through duality theory. (English) | 
| Keyword:
             | 
locally convex space | 
| Keyword:
             | 
measurable map | 
| Keyword:
             | 
random approximation | 
| Keyword:
             | 
characterization | 
| MSC:
             | 
41A65 | 
| MSC:
             | 
47H10 | 
| MSC:
             | 
47H40 | 
| MSC:
             | 
60H25 | 
| idZBL:
             | 
Zbl 1112.60050 | 
| idMR:
             | 
MR2028737 | 
| . | 
| Date available:
             | 
2008-06-06T22:42:06Z | 
| Last updated:
             | 
2012-05-10 | 
| Stable URL:
             | 
http://hdl.handle.net/10338.dmlcz/107874 | 
| . | 
| Reference:
             | 
[1] Beg I.: A characterization of random approximations.Int. J. Math. Math. Sci. 22 (1999), no. 1, 209–211.  Zbl 0921.41014, MR 1684364 | 
| Reference:
             | 
[2] Beg I., Shahzad N.: Random approximations and random fixed point theorems.J. Appl. Math. Stochastic Anal. 7 (1994), no. 2, 145–150.  Zbl 0811.47069, MR 1281509 | 
| Reference:
             | 
[3] Bharucha-Reid A. T.: Fixed point theorems in probabilistic analysis.Bull. Amer. Math. Soc. 82 (1976), no. 5, 641–557.  Zbl 0339.60061, MR 0413273 | 
| Reference:
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[4] Itoh S.: Random fixed point theorems with an application to random differential equations in Banach spaces.J. Math. Anal. Appl. 67 (1979), 261–273.  Zbl 0407.60069, MR 0528687 | 
| Reference:
             | 
[5] Lin T. C.: Random approximations and random fixed point theorems for continuous 1-set contractive random maps.Proc. Amer. Math. Soc. 123 (1995), no. 4, 1167–1176.  Zbl 0834.47049, MR 1227521 | 
| Reference:
             | 
[6] O’Regan D.: A fixed point theorem for condensing operators and applications to Hammerstein integral equations in Banach spaces.Comput. Math. Appl. 30(9) (1995), 39–49.  Zbl 0846.45006, MR 1353517 | 
| Reference:
             | 
[7] Papageorgiou N. S.: Fixed points and best approximations for measurable multifunctions with stochastic domain.Tamkang J. Math. 23 (1992), no. 3, 197–203.  Zbl 0773.60057, MR 1195311 | 
| Reference:
             | 
[8] Rao G. S., Elumalai S.: Approximation and strong approximation in locally convex spaces.Pure Appl. Math. Sci. XIX (1984), no. 1-2, 13–26.  Zbl 0552.41025, MR 0748110 | 
| Reference:
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[9] Rudin W.: Functional Analysis, McGraw-Hill Book Company.New York, 1973.  MR 0365062 | 
| Reference:
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[10] Sehgal V. M., Singh S. P.: On random approximations and a random fixed point theorem for set valued mappings.Proc. Amer. Math. Soc. 95 (1985), 91–94.  Zbl 0607.47057, MR 0796453 | 
| Reference:
             | 
[11] Tan K. K., Yuan X. Z.: Random fixed point theorems and approximations in cones.J. Math. Anal. Appl. 185 (1994), no. 2, 378–390.  MR 1283065 | 
| Reference:
             | 
[12] Thaheem A. B.: Existence of best approximations.Port. Math. 42 (1983-84), no. 4, 435–440.  MR 0836121 | 
| Reference:
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[13] Tukey J. W.: Some notes on the separation axioms of convex sets.Port. Math. 3 (1942), 95–102.   MR 0006606 | 
| . |