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Asymptotic convergence of nonlinear contraction semigroups in Hilbert space. (English) Zbl 0319.47041


MSC:

47H99 Nonlinear operators and their properties
47H05 Monotone operators and generalizations
90C99 Mathematical programming
47J05 Equations involving nonlinear operators (general)
Full Text: DOI

References:

[1] Brézis, H., Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, (Zarantonello, E. H., Contributions to Nonlinear Analysis (1971), Academic Press: Academic Press New York), 101-156 · Zbl 0278.47033
[2] Brézis, H., Propriétés régularisantes de certains semi-groupes nonlinéaires, Israel J. Math., 9, 513-534 (1971) · Zbl 0213.14903
[3] Brézis, H.; Crandall, M.; Pazy, A., Perturbations of nonlinear maximal monotone sets in Banach spaces, Comm. Pure Appl. Math., 23, 123-144 (1970) · Zbl 0182.47501
[4] Browder, F., Fixed-point theorems for noncompact mappings in Hilbert space, (Proc. Nat. Acad. Sci. U.S.A., 53 (1965)), 1272-1276 · Zbl 0125.35801
[5] Crandall, M.; Pazy, A., Semigroups of nonlinear contractions and dissipative sets, J. Functional Analysis, 3, 376-418 (1969) · Zbl 0182.18903
[6] Dafermos, C. M.; Slemrod, M., Asymptotic behavior of nonlinear contraction semigroups, J. Functional Analysis, 13, 97-106 (1973) · Zbl 0267.34062
[7] Minty, G., On the monotonicity of the gradient of a convex function, Pacific J. Math., 14, 243-247 (1964) · Zbl 0123.10601
[8] Opial, Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73, 591-597 (1967) · Zbl 0179.19902
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