Results 1 to 10 of about 8,163 (135)
The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 We show that the convergence of Mann iteration is equivalent to the convergence of Ishikawa iteration for various classes of non-Lipschitzian operators.
B. E. Rhoades, Ştefan M. Şoltuz
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Errors estimation for implicit Mann iteration
Journal of Numerical Analysis and Approximation Theory, 2006 We study the errors estimation for the implicit Mann iteration..
Ştefan M. Şoltuz
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Classical results via Mann-Ishikawa iteration
Journal of Numerical Analysis and Approximation Theory, 2007 New proofs of existence and uniqueness results for the solution of the Cauchy problem with delay are obtained by use of Mann-Ishikawa iteration.
Ştefan M. Şoltuz, Diana Otrocol
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On the Mann and Ishikawa iteration processes [PDF]
Abstract and Applied Analysis, 1996 It is shown that a result of Chidume, involving the strong convergence of the Mann iteration process for continuous strongly accretive operators, is actually a corollary to a result by Nevanlinna and Reich. It is then shown that the Nevanlinna and Reich result can be extended to the case of an Ishikawa iteration process.
Jia Yuting, Zhou Haiyun
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On a new approach of enriched operators [PDF]
HeliyonWe establish the existence and uniqueness of fixed points of generalized contractions in the setting of Banach spaces and prove the convergence of Mann iteration for this general class of mappings.
Teodor Turcanu, Mihai Postolache
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Introduction of new Picard–S hybrid iteration with application and some results for nonexpansive mappings [PDF]
Arab Journal of Mathematical Sciences, 2022 Purpose – In this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard ...
Julee Srivastava
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On Modified Halpern and Tikhonov–Mann Iterations [PDF]
Journal of Optimization Theory and Applications, 2023 AbstractWe show that the asymptotic regularity and the strong convergence of the modified Halpern iteration due to T.-H. Kim and H.-K. Xu and studied further by A. Cuntavenapit and B. Panyanak and the Tikhonov–Mann iteration introduced by H. Cheval and L. Leuştean as a generalization of an iteration due to Y. Yao et al.
Cheval, Horaţiu +2 more
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Fixed point theorems in uniformly convex Banach spaces
Ratio Mathematica, 2023 In this article, we establish a concept of fixed point result in Uniformly convex Banach space. Our main finding uses the Ishikawa iteration technique in uniformly convex Banach space to demonstrate strong convergence.
Manoj Karuppasamy, R. Jahir Hussain
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On some Mann’s type iterative algorithms [PDF]
Fixed Point Theory and Applications, 2015 AbstractFirst we present some interesting variants of Mann’s method. In the last section, we show that many existing results in the literature are concrete realizations of our general scheme under varying assumptions on the coefficients.
Luigi Muglia +4 more
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Equivalence of Certain Iteration Processes Obtained by Two New Classes of Operators
Mathematics, 2021 The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for
Mujahid Abbas +2 more
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