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On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space. (English) Zbl 0423.47023


MSC:

47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
49J40 Variational inequalities
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References:

[1] Baillon, J. B., Un théorème de type ergodique pour les contractions non linéaires dans un espace de Hilbert, C. R. Acad. Sci. Paris A-B, 280, A1511-A1514 (1975)
[2] Baillon, J. B.; Brezis, H., Une remarque sur le comportement asymptotique des semigroupes non linéaires, Houston J. Math., 2, 5-7 (1976) · Zbl 0318.47039
[3] Browder, F. E., Nonlinear variational inequalities and maximal monotone mappings in Banach spaces, Math. Ann., 183, 213-231 (1969) · Zbl 0208.39105
[4] Bruck, R. E., An iterative solution of a variational inequality for certain monotone operators in Hilbert space, Bull. Amer. Math. Soc., 81, 890-892 (1975) · Zbl 0332.49005
[5] Bruck, R. E., Corrigendum to the above, Bull. Amer. Math. Soc., 82, 353 (1976) · Zbl 0338.49003
[6] Bruck, R. E., A strongly convergent iterative solution of \(0 ϵU(x)\) for a maximal monotone operator \(U\) in Hilbert space, J. Math. Anal. Appl., 48, 114-126 (1974) · Zbl 0288.47048
[7] Darbo, G., Punti uniti in transformazioni a condominio non compatto, (Rend. Sem. Mat. Univ. Padova, 24 (1955)), 84-92 · Zbl 0064.35704
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