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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:
47H07Monotone and positive operators on ordered topological linear spaces
49J40Variational methods including 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) · Zbl 0307.47006
[2] Baillon, J. B.; Brezis, H.: Une remarque sur le comportement asymptotique des semigroupes non linéaires. Houston J. Math. 2, 5-7 (1976)
[3] Browder, F. E.: Nonlinear variational inequalities and maximal monotone mappings in Banach spaces. Math. ann. 183, 213-231 (1969) · Zbl 0208.39105
[4] Jr., R. E. Bruck: 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] Jr., R. E. Bruck: Corrigendum to the above. Bull. amer. Math. soc. 82, 353 (1976)
[6] Jr., R. E. Bruck: A strongly convergent iterative solution of $0 \epsilon U(x)$ 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, 84-92 (1955) · Zbl 0064.35704