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Iterative sequences for asymptotically quasi-nonexpansive mappings. (English) Zbl 1033.47047

Some sufficient and necessary conditions are obtained for Ishikawa iterative sequences of asymtotically quasi-nonexpansive mappings to converge to their respective fixed points.
Reviewer: S. Tersian (Russe)

MSC:

47J25 Iterative procedures involving nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.
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References:

[1] Petryshyn, W.V.; Williamson, T.E., Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings, J. math. anal. appl., 43, 459-497, (1973) · Zbl 0262.47038
[2] Gosh, M.K.; Debnath, L., Convergence of Ishikawa iterates of quasi-nonexpansive mappings, J. math. anal. appl., 207, 96-103, (1997) · Zbl 0881.47036
[3] Xu, H.K., Existence and convergence for fixed points of mappings of asymptotically nonexpansive type, Nonlinear anal., 16, 1139-1146, (1991) · Zbl 0747.47041
[4] 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
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