154 research outputs found
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 Fixed Points of The General Asymptotic Set Valued Mappings
The purpose of this paper is to introduce a new generalization of asymptotically non-expansive set-valued mapping and to discuss its demi-closeness principle. Then, under certain conditions, we prove that the sequence defined by yn+1 = tn z+ (1-tn )un , un in Gn( yn ) converges strongly to some fixed point in reflexive Banach spaces. As an application, existence theorem for an iterative differential equation as well as convergence theorems for a fixed point iterative method designed to approximate this solution is prove
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
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
Results on a faster iterative scheme for a generalized monotone asymptotically
This article devoted to present results on convergence of Fibonacci-Halpern scheme (shortly, FH) for monotone asymptotically αn-nonexpansive mapping (shortly, ma αn-n mapping) in partial ordered Banach space (shortly, POB space). Which are auxiliary theorem for demi-close's proof of this type of mappings, weakly convergence of increasing FFH-scheme to a fixed point with aid monotony of a norm and Σn+=∞1 λn= +∞, λn =min{hn , (1-hn)} where hn ⸦ (0,1) where is associated with FH-scheme for an integer n>0 more than that, convergence amounts to be strong by using Kadec-Klee property and finally, prove that this scheme is weak-w2 stable up on suitable status
S- ITERATION PROCESS FOR CONVERGENCE OF TWO ASYMPTOTICALLY NON-EXPANSIVE MAPPING IN CAT (0) SPACE
In this paper we establish some strong convergence theorem for two asymptotically non expansive mapping by modified S-iteration process under suitable conditions
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