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Ergodic convergence to a zero of the sum of monotone operators in Hilbert space. (English) Zbl 0428.47039


MSC:

47J25 Iterative procedures involving nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.
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References:

[1] Baillon, J.B, Thèse, (1978), Paris
[2] {\scJ. B. Baillon and P. L. Lions}, Convergence de suites de contractions dans un espace de Hilbert, preprint.
[3] Brézis, H; Lions, P.L, Produits infinis de résolvantes, Israel J. math., 29, 329-345, (1978) · Zbl 0387.47038
[4] Browder, F.E, On the unification of the calculus of variations and the theory of monotone nonlinear operators in Banach spaces, (), 419-425 · Zbl 0143.36902
[5] Browder, F.E, Existence and approximation of solutions of nonlinear variational inequalities, (), 1080-1086 · Zbl 0148.13502
[6] 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
[7] Bruck, R.E, On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space, J. math. anal. appl., 61, 159-164, (1977) · Zbl 0423.47023
[8] Passty, G.B, Asymptotic behavior of an implicit differencing scheme associated with accretive operators in Banach spaces, ()
[9] Rockafellar, R.T, Monotone operators and the proximal point algorithm, SIAM J. control and optimization, 14, 877-898, (1976) · Zbl 0358.90053
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