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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
[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 (1966)), 419-425 · Zbl 0143.36902
[5] Browder, F. E., Existence and approximation of solutions of nonlinear variational inequalities, (Proc. Nat. Acad. Sci. USA, 56 (1966)), 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, (Ph. D. dissertation (1978), University of Southern California: University of Southern California Los Angeles, California)
[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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