In this paper we prove a general random fixed point theorem for multivalued maps in Frechet spaces. We apply our main result to obtain some common random fixed point theorems. Our main result unifies and extends the work due to Benavides, Acedo and Xu [4], Itoh [8], Lin [12], Liu [13], Tan and Yuan [20], Xu [23], etc.
@article{107824, author = {Naseer Shahzad}, title = {Random fixed points of multivalued maps in Fr\'echet spaces}, journal = {Archivum Mathematicum}, volume = {038}, year = {2002}, pages = {95-100}, zbl = {1068.47075}, mrnumber = {1909591}, language = {en}, url = {http://dml.mathdoc.fr/item/107824} }
Shahzad, Naseer. Random fixed points of multivalued maps in Fréchet spaces. Archivum Mathematicum, Tome 038 (2002) pp. 95-100. http://gdmltest.u-ga.fr/item/107824/
Some random approximation theorems with applications, Nonlinear Anal. 35 (1999), 609–616. (1999) | MR 1656922 | Zbl 0931.60054
Random fixed points of weakly inward operators in conical shells, J. App. Math. Stochastic Anal. 8 (1995), 261–264. (1995) | MR 1342645 | Zbl 0828.47044
Applications of the proximity map to random fixed point theorems in Hilbert spaces, J. Math. Anal. Appl. 196 (1995), 606–613. (196 ) | MR 1362709
Random fixed points of set-valued operators, Proc. Amer. Math. Soc. 124 (1996), 831–838. (1996) | MR 1301487 | Zbl 0841.47032
Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc. 82 (1976), 641–657. (1976) | MR 0413273 | Zbl 0339.60061
Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660–665. (1968) | MR 0230179 | Zbl 0164.44801
Measurable relations, Fund. Math. 87 (1975), 53–72. (1975) | MR 0367142 | Zbl 0296.28003
Random fixed point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl. 67 (1979), 261–273. (1979) | MR 0528687 | Zbl 0407.60069
A random fixed point theorem for a multivalued contraction mapping, Pacific J. Math. 68 (1977), 85–90. (1977) | MR 0451228 | Zbl 0335.54036
A general theorem on selectors, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 379–403. (1965) | MR 0188994 | Zbl 0152.21403
Multivalued nonexpansive mappings with Opial’s condition, Proc. Amer. Math. Soc. 38 (1973), 286–292. (1973) | MR 0310718
Random approximations and random fixed point theorems for continuous 1-set-contractive random maps, Proc. Amer. Math. Soc. 123 (1995), 1167–1176. (1995) | MR 1227521 | Zbl 0834.47049
Some random approximations and random fixed point theorems for 1-set-contractive random operators, Proc. Amer. Math. Soc. 125 (1997), 515–521. (1997) | MR 1350953 | Zbl 0869.47031
Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 595–597. (1967) | MR 0211301 | Zbl 0179.19902
Random fixed points and random differential inclusions, Int. J. Math. Math. Sci. 11 (1988), 551–560. (1988) | MR 0947287 | Zbl 0658.60090
Functional Analysis, McGraw Hill, New York, 1973. (1973) | MR 0365062 | Zbl 0253.46001
Random fixed point theorems for various classes of 1-set-contractive maps in Banach spaces, J. Math. Anal. Appl. 203 (1996), 712–718. (1996) | MR 1417125 | Zbl 0893.47037
Random fixed points for 1-set-contractive random maps in Frechet spaces, J. Math. Anal. Appl. 231 (1999), 68–75. (1999) | MR 1676737
Random fixed points for several classes of 1-ball-contractive and 1-set-contractive random maps, J. Math. Anal. Appl. 237 (1999), 83–92. (1999) | MR 1708163 | Zbl 1115.47314
Random fixed point theorems and approximation, Stochastic Anal. Appl. 15 (1997), 103–123. (1997) | MR 1429860 | Zbl 0892.47060
Random fixed point theorems and approximation in cones, J. Math. Anal. Appl. 185 (1994), 378–390. (1994) | MR 1283065 | Zbl 0856.47036
Integration on functions with values in locally convex Suslin spaces, Trans. Amer. Math. Soc. 212 (1975), 61–81. (1975) | MR 0385067
Some random fixed point theorems for condensing and nonexpansive operators, Proc. Amer. Math. Soc. 110 (1990), 495–500. (1990) | MR 1021908 | Zbl 0716.47029
Measurability of fixed point sets of multivalued random operators, J. Math. Anal. Appl. 225 (1998), 62–72. (1998) | MR 1639289 | Zbl 0913.47057