434 research outputs found
Convergence Theorems of Three-Step Iterative Scheme for a Finite Family of Uniformly Quasi-Lipschitzian Mappings in Convex Metric Spaces
We consider a new Noor-type iterative procedure with errors for approximating the common fixed point of a finite family of uniformly quasi-Lipschitzian mappings in convex metric spaces. Under appropriate conditions, some convergence theorems are proved for such iterative sequences involving a finite family of uniformly quasi-Lipschitzian mappings. The results presented in this paper extend, improve and unify some main results in previous work
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 -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 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
Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces
Convergence of iterates with errors of uniformly quasi-Lipschitzian mappings in cone metric spaces
The aim of this paper is to consider an Ishikawa type iteration process with errors to approximate the fixed point of two uniformly quasi-Lipschitzian mappings in cone metric spaces. We also extend some fixed point results of these mappings from complete generalized convex metric spaces to cone metric spaces. Our results extend and generalize many known results
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