Iteration sequences for asymptotically quasi-nonexpansive mapping with an error member of uniform convex Banach space. (English) Zbl 1057.47057

Building on his previous results [ibid. 259, 18–24 (2001; Zbl 1001.47034)], the author proves the convergence of Ishikawa iterations for an asymptotically quasi-nonexpansive map in a uniformly convex Banach space.


47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J25 Iterative procedures involving nonlinear operators
46B20 Geometry and structure of normed linear spaces


Zbl 1001.47034
Full Text: DOI


[1] Tan, K.-K.; Xu, H. K., Fixed point iteration processes for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 122, 733-739 (1994) · Zbl 0820.47071
[2] Qihou, L., Iterative sequences for asymptotically quasi-nonexpansive mapping with error member, J. Math Anal. Appl., 259, 18-24 (2001) · Zbl 1001.47034
[3] Schu, J., Iterative construction of fixed points of strictly quasicontractive mappings, Appl. Anal., 40, 67-72 (1991) · Zbl 0697.47061
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