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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, (), 84-92 · Zbl 0064.35704
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