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Weak convergence theorems for nonexpansive mappings in Banach spaces. (English) Zbl 0423.47026


MSC:

47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H06 Nonlinear accretive operators, dissipative operators, etc.
47J25 Iterative procedures involving nonlinear operators
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References:

[1] {\scJ.-B. Baillon}, preprint.
[2] {\scJ.-B. Baillon, R. E. Bruck, and S. Reich}, On the asymptotic behavior of non-expansive mappings and semigroups in Banach spaces, Houston. J. Math., in press.
[3] Brézis, H; Browder, F.E, Nonlinear ergodic theorems, Bull. amer. math. soc., 82, 959-961, (1976) · Zbl 0339.47029
[4] Browder, F.E, Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. amer. math. soc., 74, 660-665, (1968) · Zbl 0164.44801
[5] {\scR. E. Bruck}, On the almost convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak ω-limit set, Israel J. Math., in press. · Zbl 0367.47037
[6] {\scR. E. Bruck}, A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces, to appear. · Zbl 0423.47024
[7] {\scR. E. Bruck and S. Reich}, Nonexpansive projections and resolvents of accretive operators in Banach spaces, Houston J. Math., in press. · Zbl 0383.47035
[8] Groetsch, C.W, A note on segmenting Mann iterates, J. math. anal. appl., 40, 369-372, (1972) · Zbl 0244.47042
[9] Lorentz, G.G, A contribution to the theory of divergent series, Acta math., 80, 167-190, (1948) · Zbl 0031.29501
[10] Reich, S, Fixed points via Toeplitz iteration, Bull. Calcutta math. soc., 65, 203-207, (1973) · Zbl 0322.47035
[11] Reich, S, Nonlinear evolution equations and nonlinear ergodic theorems, Nonlinear anal., 1, 319-330, (1977) · Zbl 0359.34059
[12] Reich, S, Almost convergence and nonlinear ergodic theorems, J. approximation theory, 24, 269-272, (1978) · Zbl 0404.47032
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