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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Classical results via Mann-Ishikawa iteration [PDF]
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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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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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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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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Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu operators
Fixed Point Theory and Applications, 2006 The purpose of this paper is to show that the Mann iteration converges faster than the Ishikawa iteration for the class of Zamfirescu operators of an arbitrary closed convex subset of a Banach space.
Vara Prasad KNVV, Babu GVR
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Zenali Iteration Method For Approximating Fixed Point of A δZA - Quasi Contractive mappings
Ibn Al-Haitham Journal for Pure and Applied Sciences, 2021 This article will introduce a new iteration method called the zenali iteration method for the approximation of fixed points. We show that our iteration process is faster than the current leading iterations like Mann, Ishikawa, oor, D- iterations, and *-
Zena Hussein Maibed, Ali Qasem Thajil
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Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators
Fixed Point Theory and Applications, 2004 In the class of quasi-contractive operators satisfying Zamfirescu's conditions, the most used fixed point iterative methods, that is, the Picard, Mann, and Ishikawa iterations, are all known to be convergent to the unique fixed point. In this paper, the
Berinde Vasile
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Generation of Antifractals via Hybrid Picard-Mann Iteration
IEEE Access, 2020 The aim of this paper is to generate antifractals using fixed point iterative algorithms, i.e., we aim to generate anti Julia sets, tricorns and multicorns for the anti-polynomial z → z̅k +c of the complex polynomial zk +c, for k ≥ 2.
Wei Wang +3 more
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Weak Convergence of Two Iteration Schemes in Banach Spaces [PDF]
Engineering and Technology Journal, 2019 In this paper, we established weak convergence theorems by using appropriate conditions for approximating common fixed points and equivalence between the convergence of the Picard-Mann iteration scheme and Liu et al iteration scheme in Banach spaces.
Salwa Abed, Zahraa Mohamed Hasan
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