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Strong convergence to common fixed points of countable relatively quasi-nonexpansive mappings. (English) Zbl 1203.47061

Summary: We prove that a sequence generated by the monotone CQ-method converges strongly to a common fixed point of a countable family of relatively quasi-nonexpansive mappings in a uniformly convex and uniformly smooth Banach space. Our result is applicable to a wide class of mappings.

MSC:

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

[1] doi:10.2307/2032162 · Zbl 0050.11603 · doi:10.2307/2032162
[2] doi:10.1016/0022-247X(79)90024-6 · Zbl 0423.47026 · doi:10.1016/0022-247X(79)90024-6
[3] doi:10.1016/j.na.2003.10.010 · Zbl 1059.47060 · doi:10.1016/j.na.2003.10.010
[4] doi:10.1007/BF02757276 · Zbl 0314.47031 · doi:10.1007/BF02757276
[5] doi:10.1016/S0022-247X(02)00458-4 · Zbl 1035.47048 · doi:10.1016/S0022-247X(02)00458-4
[7] doi:10.1016/j.na.2007.04.008 · Zbl 1220.47122 · doi:10.1016/j.na.2007.04.008
[11] doi:10.1155/2007/21972 · Zbl 1156.47055 · doi:10.1155/2007/21972
[12] doi:10.1155/S1687182004310089 · Zbl 1088.47054 · doi:10.1155/S1687182004310089
[13] doi:10.1016/j.jat.2005.02.007 · Zbl 1071.47063 · doi:10.1016/j.jat.2005.02.007
[15] doi:10.1016/j.jat.2007.04.014 · Zbl 1137.47056 · doi:10.1016/j.jat.2007.04.014
[16] doi:10.1016/j.na.2006.08.021 · Zbl 1124.47046 · doi:10.1016/j.na.2006.08.021
[17] doi:10.1016/j.na.2006.08.032 · Zbl 1130.47045 · doi:10.1016/j.na.2006.08.032
[19] doi:10.1137/S105262340139611X · Zbl 1101.90083 · doi:10.1137/S105262340139611X
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