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Itoh, Shigeru

Random fixed point theorems with an application to random differential equations in Banach spaces. (English) Zbl 0407.60069

J. Math. Anal. Appl. 67, 261-273 (1979).
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Cited in 13 Reviews
Cited in 144 Documents

MSC:

60H25 Random operators and equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
54C60 Set-valued maps in general topology
47H10 Fixed-point theorems

Keywords:

random fixed point theorem; fixed point theorem; random differential equation; measurable multivalued mapping

Citations:

Zbl 0152.214; Zbl 0296.28003; Zbl 0174.460
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Full Text: DOI

References:

[1] Ambrosetti, A., Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, (Rend. Sem. Mat. Univ. Padova, 39 (1967)), 349-361 · Zbl 0174.46001
[2] Bharucha-Reid, A. T., Fixed-point theorems in probabilistic analysis, Bull. Amer. Math. Soc., 82, 641-657 (1976) · Zbl 0339.60061
[3] Bharucha-Reid, A. T., Random Integral Equations (1972), Academic Press: Academic Press New York/London · Zbl 0327.60040
[4] Bohnenblust, H. F.; Karlin, S., On a theorem of Ville, (Kuhn, H. W.; Tucker, A. W., Contributions to the Theory of Games I (1950), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J), 155-160 · Zbl 0041.25701
[5] Browder, F. E., Fixed-point theorems for non-compact mappings in Hilbert space, (Proc. Nat. Acad. Sci. U.S.A., 53 (1965)), 1272-1276 · Zbl 0125.35801
[6] Browder, F. P., Convergence of approximants to fixed points of nonexpansive non-linear mappings in Banach spaces, Arch. Rational Mech. Anal., 24, 82-90 (1967) · Zbl 0148.13601
[7] Browder, F. E., Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc., 74, 660-665 (1968) · Zbl 0164.44801
[8] Castaing, C., Sur les multi-applications measurables, Rev. Française Informat. Recherche Opérationnelle, 1, 91-126 (1967) · Zbl 0153.08501
[9] Dunford, N.; Schwartz, J. T., Linear Operators (1958), Interscience: Interscience New York, Part I · Zbl 0084.10402
[10] Furi, M.; Vignoli, A., Fixed points for densifying mappings, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 47, 465-467 (1969) · Zbl 0193.51402
[11] Furi, M.; Vignoli, A., On α-nonexpansive mappings and fixed points, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 48, 195-198 (1970) · Zbl 0197.11806
[12] Hanš, O., Reduzierende zufällige Transformationen, Czechoslovak Math. J., 7, 154-158 (1957) · Zbl 0090.34804
[13] Hanš, O., Random fixed point theorems, (Transactions of the Fist Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (1957), Publishing House of the Czechoslovak Academy of Sciences: Publishing House of the Czechoslovak Academy of Sciences Prague), 105-125
[14] Hanš, O., Random operator equations, (Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. II (1961), Univ. of California Press: Univ. of California Press Berkeley), 185-202, Part I · Zbl 0132.12402
[15] Hille, K.; Phillips, R. S., Functional Analysis and Semi-Groups (1957), Amer. Math. Soc: Amer. Math. Soc Providence, R.I · Zbl 0078.10004
[16] Himmelberg, C. J., Measurable relations, Fund. Math., 87, 53-72 (1975) · Zbl 0296.28003
[17] S. ItohFund. Math.; S. ItohFund. Math. · Zbl 0412.54054
[18] Itoh, S., A random fixed point theorem for a multivalued contraction mapping, Pacific J. Math., 68, 85-90 (1977) · Zbl 0335.54036
[19] Itoh, S.; Takahashi, W., Single-valued mappings, multivalued mappings and fixed-point theorems, J. Math. Anal. Appl., 59, 514-521 (1977) · Zbl 0351.47040
[20] Kannan, R.; Salehi, H., Random solutions of nonlinear differential equations, Boll. Un. Mat. Ital. (4), 12, 209-213 (1975) · Zbl 0383.60058
[21] Krasnosel’skii, M. A., Two remarks on the method of successive approximations, Uspehi Mat. Nauk, 10, No. 1 (63), 123-127 (1955), (Russian) · Zbl 0064.12002
[22] Kuratowski, K., (Topology, Vol. 1 (1966), PWN-Polish Scientific Publishers and Academic Press: PWN-Polish Scientific Publishers and Academic Press Warsaw and New York) · Zbl 0158.40802
[23] Kuratowski, K.; Ryll-Nardzewski, C., A general theorem on selectors, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 13, 397-403 (1965) · Zbl 0152.21403
[24] Dozo, E. Lami, Multivalued nonexpansive mappings and Opial’s condition, (Proc. Amer. Math. Soc., 38 (1973)), 286-292 · Zbl 0268.47060
[25] Michael, E., Topologies on spaces of subsets, Trans. Amer. Math. Soc., 71, 152-182 (1951) · Zbl 0043.37902
[26] Mukherjea, A., Transformations aléatoires séparables: Théorème du point fixe aléatoire, C. R. Acad. Sci. Paris, 263, 393-395 (1966) · Zbl 0139.33404
[27] Nussbaum, R. D., The fixed point index for local condensing maps, Ann. Math. Pura Appl., 89, 217-258 (1971) · Zbl 0226.47031
[28] Opial, Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73, 591-597 (1967) · Zbl 0179.19902
[29] Parthasarathy, K. R., Probability Measures on Metric Spaces (1967), Academic Press: Academic Press New York/London · Zbl 0153.19101
[30] Petryshyn, W. V.; Fitzpatrick, P. M., Fixed-point theorems for multivalued noncompact inward maps, J. Math. Anal. Appl., 46, 756-767 (1974) · Zbl 0287.47038
[31] Phelps, R. R., Convex sets and nearest points, (Proc. Amer. Math. Soc., 8 (1957)), 790-797 · Zbl 0078.35701
[32] Rao, B. L.S. Prakasa, Stochastic integral equations of mixed type II, J. Math. Phys. Sci., 7, 245-260 (1973) · Zbl 0273.60038
[33] Reinermann, J., Fixpunktsätze vom Krasnoselski-Typ, Math. Z., 119, 339-344 (1971) · Zbl 0204.45802
[34] Špaček, A.; Gleichungen, Zufällige, Czechoslovak Math. J., 5, 462-466 (1955) · Zbl 0068.32701
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