On unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in Banach spaces

In this paper, we unify all know iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptotically $I$-nonexpansive mappings. Note that such a scheme contains as a particular case of the method introduced in [C.E. Chidume, E.U. Ofoedu, \textit{Inter. J. Math. & Math. Sci.} \textbf{2009}(2009) Article ID 615107, 17p]. We construct examples of total asymptotically nonexpansive mappings which are not asymptotically nonexpansive. Note that no such kind of examples were known in the literature. We prove the strong convergence theorems for such iterative process to a common fixed point of the finite family of total asymptotically $I-$nonexpansive and total asymptotically nonexpansive mappings, defined on a nonempty closed convex subset of uniformly convex Banach spaces. Moreover, our results extend and unify all known results.Comment: 22 pages, Journal of Applied Mathematics (in press

A note on strong convergence to common fixed points of nonexpansive mappings in Hilbert spaces

The aim of this paper is to investigate the links between ${\cal T}_C$-class algorithms, CQ Algorithm and shrinking projection methods. We show that strong convergence of these algorithms are related to coherent ${\cal T}_C$-class sequences of mapping. Some examples dealing with nonexpansive finite set of mappings and nonexpansive semigroups are given. They extend some existing theorems