## 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

### Citations:

Zbl 0369.47030; Zbl 0423.47025; Zbl 0407.47035
Full Text:

### 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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