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

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H06Accretive operators, dissipative operators, etc. (nonlinear)
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References:
[1] Baillon, J. B.: Thèse. (1978)
[2] J. 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. Proc. nat. Acad. sci. USA 56, 419-425 (1966) · Zbl 0143.36902
[5] Browder, F. E.: Existence and approximation of solutions of nonlinear variational inequalities. Proc. nat. Acad. sci. USA 56, 1080-1086 (1966) · Zbl 0148.13502
[6] 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
[7] Jr., R. E. Bruck: 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. Ph. D. Dissertation (1978)
[9] Rockafellar, R. T.: Monotone operators and the proximal point algorithm. SIAM J. Control and optimization 14, 877-898 (1976) · Zbl 0358.90053