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Zbl 1086.47044
Chang, S.S.; Tan, K.K.; Lee, H.W.J.; Chan, Chi Kin
On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings.
(English)
[J] J. Math. Anal. Appl. 313, No. 1, 273-283 (2006). ISSN 0022-247X

The authors study the weak and strong convergence of the implicit iteration sequences $\{ x_{n}\}$ defined by: \align x_{n}&= \alpha _{n}x_{n-1} + (1-\alpha _{n})T^{k(n)}_{i(n)}x_{n} + u_{n}, \quad n \geq 1\quad\text{and}\\ x_{n}&=\alpha _{n}x_{n-1} + (1- \alpha _{n})T^{k(n)}_{i(n)}x_{n},\quad n \geq 1\endalign to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in real uniformly convex Banach spaces. Their results extend and improve results of several other authors.
[Edward Prempeh (Kumasi)]
MSC 2000:
*47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: asymptotically nonexpansive mapping; nonexpansive mapping; implicit iterative sequence with errors for a finite family; common fixed point; Opial condition; demi-closed principle; semi-compactness

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