433 research outputs found

    Convergence Theorems of Three-Step Iterative Scheme for a Finite Family of Uniformly Quasi-Lipschitzian Mappings in Convex Metric Spaces

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    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

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    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 II-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 II-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

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    Convergence of iterates with errors of uniformly quasi-Lipschitzian mappings in cone metric spaces

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    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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