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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

47H07Monotone and positive operators on ordered topological linear spaces
49J40Variational methods including variational inequalities
Full Text: DOI
[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