×

Iterative sequences for asymptotically quasi-nonexpansive mappings with error member. (English) Zbl 1001.47034

The paper concerns convergence of Ishikawa iterative sequences \((x_n)_n\) with error members for asymptotically quasi-nonexpansive mappings \(T:E\to E\). Here \(E\) is a nonempty closed convex set of a Banach space and the set \(F(T)\) of fixed points of \(T\) is nonempty. The main results state \((x_n)_n\) converges to a fixed point of \(T\) if and only if \(\liminf_{n\to\infty}d(x_n,F(T))=0\).

MSC:

47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J25 Iterative procedures involving nonlinear operators
PDFBibTeX XMLCite
Full Text: DOI

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] Ghosh, M. K.; Debnath, L., Convergence of Ishikawa iterates of quasi-nonexpansive mappings, J. Math. Anal. Appl., 207, 96-103 (1997) · Zbl 0881.47036
[3] Liu, Qihou, Iterative sequences for asymptotic quasi-nonexpansive mapping, J. Math. Anal. Appl, in press.; Liu, Qihou, Iterative sequences for asymptotic quasi-nonexpansive mapping, J. Math. Anal. Appl, in press. · Zbl 1033.47047
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.