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Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces. (English) Zbl 0427.47049

MSC:
47H20Semigroups of nonlinear operators
References:
[1]J. B. Baillon, R. E. Bruck and S. Reich,On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces, Houston J. Math., to appear.
[2]H. Brezis,Monotonicity methods in Hilbert space and some applications to nonlinear partial differential equations, inContributions to Nonlinear Functional Analysis (E. H. Zarantonello, ed.), Academic Press, New York, 1971, pp. 101–156.
[3]H. Brezis,Opérateurs Maximaux Monotones et Semigroupes de Contractions dans les Espaces de Hilbert, North-Holland Publishing Co., Amsterdam, 1973.
[4]H. Brezis and P. L. Lions, Produits infinis de résolvantes, Israel J. Math.29 (1978), 329–345. · Zbl 0387.47038 · doi:10.1007/BF02761171
[5]F. E. Browder,Nonlinear accretive operators in Banach spaces, Bull. Amer. Math. Soc.73 (1967), 470–476. · Zbl 0159.19905 · doi:10.1090/S0002-9904-1967-11786-5
[6]R. E. Bruck,The iterative solution of the equation y x+Tx for a monotone operator T in Hilbert space, Bull. Amer. Math. Soc.79 (1973), 1258–1261. · Zbl 0275.47033 · doi:10.1090/S0002-9904-1973-13404-4
[7]R. E. Bruck,A strongly convergent iterative solution of the equation 0 U (x) for a maximal monotone operator U in Hilbert space J. Math. Anal. Appl.48 (1974), 114–126. · Zbl 0288.47048 · doi:10.1016/0022-247X(74)90219-4
[8]R. E. Bruck and S. Reich,Nonexpansive projections and resolvents of accretive operators in Banach spaces, Houston J. Math.3 (1977), 459–470.
[9]M. D. Canon and C. D. Cullum,A tight upper bound on the rate of convergence of the Frank-Wolfe algorithm, SIAM J. Control6 (1968), 509–516. · Zbl 0186.24002 · doi:10.1137/0306032
[10]M. G. Crandall and T. M. Liggett,Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math.93 (1971), 265–298. · Zbl 0226.47038 · doi:10.2307/2373376
[11]M. G. Crandall and A. Pazy,On the range of accretive operators, Israel J. Math.27 (1977), 235–246. · Zbl 0355.47039 · doi:10.1007/BF02756485
[12]J. C. Dunn,Iterative construction of fixed points for multivalued operators of the monotone type, J. Functional Analysis27 (1978), 38–50. · Zbl 0422.47033 · doi:10.1016/0022-1236(78)90018-6
[13]A. Pazy,On the asymptotic behavior of semigroups of nonlinear contractions in Hilbert space, J. Functional Analysis27 (1978), 292–307. · Zbl 0377.47045 · doi:10.1016/0022-1236(78)90010-1
[14]A. Pazy,Strong convergence of semigroups of nonlinear contractions in Hilbert space, MRC Report # 1828, 1978.
[15]S. Reich,An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Analysis2 (1978), 85–92. · Zbl 0375.47032 · doi:10.1016/0362-546X(78)90044-5
[16]S. Reich,Iterative methods for accretive sets, Proc. Conf. on Nonlinear Equations, Academic Press, to appear.
[17]S. Reich.Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., to appear.
[18]R. T. Rockafellar,Monotone operators and the proximal point algorithm, SIAM J. Control and Optimization14 (1976), 877–898. · Zbl 0358.90053 · doi:10.1137/0314056
[19]I. Singer,Best Approximation in Normed Linear Spaces, Springer, Berlin, 1970.