×

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


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
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ambrosetti, A, Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, (), 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 New York/London · Zbl 0327.60040
[4] Bohnenblust, H.F; Karlin, S, On a theorem of ville, (), 155-160 · Zbl 0041.25701
[5] Browder, F.E, Fixed-point theorems for non-compact mappings in Hilbert space, (), 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 New York, Part I
[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, (), 105-125
[14] Hanš, O, Random operator equations, (), 185-202, Part I
[15] Hille, K; Phillips, R.S, Functional analysis and semi-groups, (1957), Amer. Math. Soc Providence, R.I
[16] Himmelberg, C.J, Measurable relations, Fund. math., 87, 53-72, (1975) · Zbl 0296.28003
[17] {\scS. Itoh}, Some fixed point theorems in metric spaces, Fund. Math., in press. · 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)
[22] Kuratowski, K, ()
[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, (), 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 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, (), 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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.