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Reich, Simeon

On the asymptotic behavior of nonlinear semigroups and the range of accretive operators. (English) Zbl 0457.47053

J. Math. Anal. Appl. 79, 113-126 (1981).
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Cited in 5 Reviews
Cited in 65 Documents

MSC:

47H20 Semigroups of nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.

Keywords:

accretive operator; nonexpansive nonlinear semigroup

Citations:

Zbl 0275.47034; Zbl 0337.47027; Zbl 0225.54032; Zbl 0364.93031
Cite Review PDF
Full Text: DOI

References:

[1] Baillon, J. B.; Bruck, R. E.; Reich, S., On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces, Houston J. Math., 4, 1-9 (1978) · Zbl 0396.47033
[2] Bewley, T.; Kohlberg, E., The asymptotic theory of stochastic games, Math. Operations Res., 1, 197-208 (1976) · Zbl 0364.93031
[3] Brezis, H., Opérateurs Maximaux Monotones et Semigroupes de Contractions dans les Espaces de Hilbert (1973), North-Holland: North-Holland Amsterdam · Zbl 0252.47055
[4] Brezis, H.; Lions, P. L., Produits infinis de résolvantes, Israel J. Math., 29, 329-345 (1978) · Zbl 0387.47038
[6] Bruck, R. E.; Reich, S., Nonexpansive projections and resolvents of accretive operators in Banach spaces, Houston J. Math., 3, 459-470 (1977) · Zbl 0383.47035
[7] Corduneanu, A., A note on the minimum property of cl(R(A)) for a monotone mapping in a real Hilbert space, Atti Accad. Naz. Lincei, 53, 56-59 (1972) · Zbl 0262.47044
[8] Crandall, M. G.; Liggett, T. M., Generation of semigroups of nonlinear transformations on general Banach spaces, Amer. J. Math., 93, 265-298 (1971) · Zbl 0226.47038
[9] Cudia, D. F., The geometry of Banach spaces, smoothness, Trans. Amer. Math. Soc., 110, 284-314 (1964) · Zbl 0123.30701
[10] Day, M. M., Normed Linear Spaces (1973), Springer: Springer Berlin · Zbl 0268.46013
[11] Edelstein, M., On nonexpansive mappings of Banach spaces, (Proc. Cambridge Philos. Soc., 60 (1964)), 439-447 · Zbl 0196.44603
[12] Fan, K.; Glicksberg, I., Some geometric properties of the spheres in a normed linear space, Duke Math. J., 25, 553-568 (1958) · Zbl 0084.33101
[15] Morosanu, B., Asymptotic behavior of resolvents for a monotone mapping in a Hilbert space, Atti Accad. Naz. Lincei, 61, 565-570 (1976) · Zbl 0403.47024
[16] Nevanlinna, O., Global iteration schemes for monotone operators, Nonlinear Analysis, 3, 505-514 (1979) · Zbl 0439.47043
[17] Pazy, A., Asymptotic behavior of contractions in Hilbert space, Israel J. Math., 9, 235-240 (1971) · Zbl 0225.54032
[18] Pazy, A., On the asymptotic behavior of semigroups of nonlinear contractions in Hilbert space, J. Functional Analysis, 27, 292-307 (1978) · Zbl 0377.47045
[20] Reich, S., Asymptotic behavior of contractions in Banach spaces, J. Math. Anal. Appl., 44, 57-70 (1973) · Zbl 0275.47034
[21] Reich, S., Some fixed point problems, Atti Accad. Naz. Lincei, 57, 194-198 (1974) · Zbl 0329.47019
[22] Reich, S., Asymptotic behavior of semigroups of nonlinear contractions in Banach spaces, J. Math. Anal. Appl., 53, 277-290 (1976) · Zbl 0337.47027
[24] Reich, S., Extension problems for accretive sets in Banach spaces, J. Functional Analysis, 26, 378-395 (1977) · Zbl 0378.47037
[25] Reich, S., Nonlinear evolution equations and nonlinear ergodic theorems, Nonlinear Analysis, 1, 319-330 (1977) · Zbl 0359.34059
[26] Reich, S., A remark on the minimum property, Atti Accad. Naz. Lincei, 62, 740-741 (1977) · Zbl 0379.47039
[27] Reich, S., On infinite products of resolvents, Atti Accad. Naz. Lincei, 63, 338-340 (1977) · Zbl 0407.47034
[28] Reich, S., Product formulas, nonlinear semigroups, and accretive operators, J. Functional Analysis, 36, 147-168 (1980) · Zbl 0437.47048
[29] Reich, S., Asymptotic behavior of resolvents in Banach spaces, Atti Accad. Naz. Lincei, 67, 27-30 (1979) · Zbl 0462.47049
[30] Reich, S., A solution to a problem on the asymptotic behavior of nonexpansive mappings and semigroups, (Proc. Japan Acad., 56 (1980)), 85-87 · Zbl 0454.47059
[31] Rockafellar, R. T., Monotone operators and the proximal point algorithm, SIAM J. Control Optimization, 14, 877-898 (1976) · Zbl 0358.90053
[32] Shapley, L. S., Stochastic games, (Proc. Nat. Acad. Sci. USA, 39 (1953)), 1095-1100 · Zbl 0051.35805
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