[PDF] Top 20 On the equivalence of Mann and Ishikawa iteration methods
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On the equivalence of Mann and Ishikawa iteration methods
... A reasonable conjecture is that, whenever T is a function for which Mann iteration converges, so does the Ishikawa iteration. Given the large variety of functions and spaces, such a global ... See full document
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The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions
... M(x, y) : = max x − y , x − Tx , y − T y , x − T y , y − Tx . (1.4) In [4], the following conjecture was given: “if the Mann iteration converges, then so does the Ishikawa iteration.” In a ... See full document
5
The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ strongly accretive operators in uniformly smooth Banach spaces
... the Mann iteration method, the Mann iteration method with errors, the Ishikawa iteration method, and the Ishikawa iteration method with errors to approximate fixed ... See full document
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The Equivalence between -Stabilities of The Krasnoselskij and The Mann Iterations
... the equivalence between the T-stabilities of Mann and Ishikawa iterations, respectively, for modified Mann-Ishikawa iterations was shown in ...the equivalence between the ... See full document
7
The equivalence between the convergence of the modified Mann and Ishikawa iterations for asymptotically pseudocontractive mappings obtained by dropping the bounded assumption
... the equivalence of convergence between the modified Mann and Ishikawa iterations with errors for an asymptotically pseudocontractive mapping under the condition of removing the bounded ... See full document
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The equivalence of Mann iteration and Ishikawa iteration for ψ uniformly pseudocontractive or ψ uniformly accretive maps
... the Mann iteration converges, then so does the Ishikawa ...the equivalence between Mann and Ishikawa iterations for several classes of ...of Mann iteration is ... See full document
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Remarks of Equivalence among Picard, Mann, and Ishikawa Iterations in Normed Spaces
... show that the convergence of Picard iteration schemes is equivalent to the convergence of the Mann iteration for Zamfirescu operators in normed spaces. The result improves ones announced by S¸oltuz ... See full document
5
The equivalence of Mann iteration and Ishikawa iteration for non Lipschitzian operators
... consider Mann iteration and Ishikawa iteration with the same initial point and with the conditions lim n→∞ α n = 0, lim n→∞ β n = 0, ... See full document
7
Equivalence of semistability of Picard, Mann, Krasnoselskij and Ishikawa iterations
... Corollary . Let X be a cone Banach space, P be a normal cone and T be a quasi- contraction mapping of X with < λ < /. Then T has a unique fixed point in X and the Picard, Mann, Krasnoselskij and ... See full document
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On Equivalence of Some Iterations Convergence for Quasi-Contraction Maps in Convex Metric Spaces
... We show the equivalence of the convergence of Picard and Krasnoselskij, Mann, and Ishikawa iterations for the quasi-contraction mappings in convex metric spaces.. 1.2.[r] ... See full document
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A comparative study on the convergence rate of some iteration methods involving contractive mappings
... via iteration meth- ods is extensively studied in this ...Picard iteration converges faster than the Mann iteration for a class of quasi-contractive operators ...the Mann ... See full document
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Strong convergence theorems and rate of convergence of multi-step iterative methods for continuous mappings on an arbitrary interval
... the Mann and Ishikawa iterations to a solution of ...the Ishikawa iteration converges fas- ter than the Mann iteration for the class of continuous and nondecreasing ...the ... See full document
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Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps
... and Mann iterations were developed to obtain fixed point iteration methods which converge for some operators, such as nonexpansive ones, for which Picard iteration ...fails. Ishikawa ... See full document
12
Weak and strong convergence of an iterative algorithm for Lipschitz pseudo-contractive maps in Hilbert spaces
... the Mann iteration does not always ...the Mann sequence fails to ...the Ishikawa iteration sequence {x n } ∞ n=1 generated from arbitrary x 1 ∈ K ... See full document
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Strong convergence theorems for multivalued $alpha$-demicontractive and $alpha$-hemicontractive mappings
... the Mann iteration process to fixed points of demicontractive type mappings have studied by many authors (see ...the Mann [9] iteration do not converge to a fixed point of hemicontractive ... See full document
6
Two Step Modified Ishikawa Iteration Scheme for Multi-Valued Mappings in CAT(0) Space
... the Mann and Ishikawa iteration schemes for multi- valued mappings and proved that these schemes for a multi-valued map T with a fixed point p converges to a fixed point q of T under certain ...the ... See full document
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On the error estimation and T stability of the Ishikawa iteration for strongly demicontractive mappings
... of Ishikawa iteration and some strong convergence theorems of strongly demicontractive mappings are first ...the Ishikawa iteration and the Mann iteration are discussed in some ... See full document
12
The convergence of the modified Mann and Ishikawa iterations in Banach spaces
... nontrivial Mann iteration failing to converge while Ishikawa iteration ...the Mann (modified Mann) and Ishikawa (modified Ishikawa) iterations (with errors) converge ... See full document
12
Ishikawa iteration process with errors for nonexpansive mappings
... 1. Introduction. Let C be a closed convex subset of a Banach space X and T : C → C be a nonexpansive mapping (i.e., T x−T y ≤ x −y for all x, y in C). Recently, Deng and Li [1] introduced an Ishikawa ... See full document
5
New iteration scheme for numerical reckoning fixed points of nonexpansive mappings
... In recent years, Definition . has been used as a standard tool to compare the fastness of two fixed point iterations. Using this technique Sahu [] established that the Agarwal et al. iteration (.) converges ... See full document
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