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

摘要

In this paper, we unify all know iterative methods by introducing a newexplicit iterative scheme for approximation of common fixed points of finitefamilies of total asymptotically $I$-nonexpansive mappings. Note that such ascheme 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) ArticleID 615107, 17p]. We construct examples of total asymptotically nonexpansivemappings which are not asymptotically nonexpansive. Note that no such kind ofexamples were known in the literature. We prove the strong convergence theoremsfor such iterative process to a common fixed point of the finite family oftotal asymptotically $I-$nonexpansive and total asymptotically nonexpansivemappings, defined on a nonempty closed convex subset of uniformly convex Banachspaces. Moreover, our results extend and unify all known results.