On Picard–Krasnoselskii Hybrid Iteration Process in Banach Spaces
Journal of Mathematics, 2020 In this research, we prove strong and weak convergence results for a class of mappings which is much more general than that of Suzuki nonexpansive mappings on Banach space through the Picard–Krasnoselskii hybrid iteration process.
Thabet Abdeljawad +2 more
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Distributed Banach–Picard Iteration for Locally Contractive Maps
IEEE Transactions on Automatic Control, 2023 The Banach-Picard iteration is widely used to find fixed points of locally contractive (LC) maps. This paper extends the Banach-Picard iteration to distributed settings; specifically, we assume the map of which the fixed point is sought to be the average of individual (not necessarily LC) maps held by a set of agents linked by a communication network ...
Francisco Andrade +2 more
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Stable Iteration Procedures in Metric Spaces which Generalize a Picard-Type Iteration [PDF]
Fixed Point Theory and Applications, 2010 This paper investigates the stability of iteration procedures defined by continuous functions acting on self-maps in continuous metric spaces. Some of the obtained results extend the contraction principle to the use of altering-distance functions and ...
De la Sen M
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Convergence analysis of Suzuki's generalized nonexpansive mappings using the Picard-Abbas iteration process. [PDF]
PLoS ONEThis manuscript investigates the convergence behavior of Suzuki's generalized nonexpansive mappings using the recently introduced Picard-Abbas iteration process.
Bashir Nawaz +4 more
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T-Stability of Picard Iteration in Metric Spaces [PDF]
Fixed Point Theory and Applications, 2008 We establish a general result for the stability of Picard's iteration. Several theorems in the literature are obtained as special cases.
Yuan Qing, B. E. Rhoades
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Generation of Antifractals via Hybrid Picard-Mann Iteration [PDF]
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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Estimating the Local Radius of Convergence for Picard Iteration [PDF]
Algorithms, 2017 In this paper, we propose an algorithm to estimate the radius of convergence for the Picard iteration in the setting of a real Hilbert space. Numerical experiments show that the proposed algorithm provides convergence balls close to or even identical to ...
Ştefan Măruşter
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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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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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Some convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operators [PDF]
Mathematica Bohemica, 2019 We study some qualitative features like convergence, stability and data dependency for Picard-S iteration method of a quasi-strictly contractive operator under weaker conditions imposed on parametric sequences in the mentioned method. We compare the rate
Müzeyyen Ertürk, Faik Gürsoy
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