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On the Local convergence of two-step Newton type Method in Banach Spaces under generalized Lipschitz Conditions [article]

Akanksha Saxena, J. P. Jaiswal
2021 arXiv   pre-print
The motive of this paper is to discuss the local convergence of a two-step Newton type method of convergence rate three for solving nonlinear equations in Banach spaces.  ...  Also, some results on convergence of the same method in Banach spaces are established under the assumption that the derivative of the operators satisfies the radius or center Lipschitz condition with a  ...  Further, Wang and Li [16] derived some results on convergence of Newton's method in Banach spaces when derivative of the operators satisfies the radius or center Lipschitz condition but with a weak L-average  ... 
arXiv:2101.01361v1 fatcat:hskkbtrsojblzjwxgo7lviixhu

General iterative algorithms for solving mixed quasi-variational-like inclusions

Lu-Chuan Zeng, Qamrul Hasan Ansari, Jen-Chih Yao
2008 Computers and Mathematics with Applications  
Appl. 49 (2005) 857-869] to develop iterative algorithms for finding the approximate solutions of a mixed quasi-variational-like inclusion problem (in short, MQVLIP) in the setting of Banach spaces.  ...  Yao, Existence and algorithm of solutions for mixed quasi-variationallike inclusions in Banach spaces, Comput. Math.  ...  They also proved the existence of a unique solution to MQVLIP under weak assumptions in reflexive Banach spaces and also provided the convergence criteria of approximate solutions to the exact solution  ... 
doi:10.1016/j.camwa.2008.05.016 fatcat:oc3to3mftjhpdckbeljsenmyme

On the Local Convergence of Two-Step Newton Type Method in Banach Spaces Under Generalized Lipschitz Conditions

Akanksha Saxena, Ioannis K. Argyros, Jai P. Jaiswal, Christopher Argyros, Kamal R. Pardasani
2021 Mathematics  
The motive of this paper is to discuss the local convergence of a two-step Newton-type method of convergence rate three for solving nonlinear equations in Banach spaces.  ...  Also, some results on convergence of the same method in Banach spaces are established under the assumption that the derivative of the operators satisfies the radius or center Lipschitz condition with a  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math9060669 fatcat:2g47wt55ebe7ndnq3ppuqvlc5u

High Convergence Order Q-Step Methods for Solving Equations and Systems of Equations

Ioannis K. Argyros, Santhosh George
2020 Contemporary Mathematics  
This way we extend the applicability of these methods. The analysis includes computable radius of convergence as well as error bounds based on Lipschitz-type conditions not given in earlier studies.  ...  In the present study, we introduce generalized multi-step high order methods for solving nonlinear equations.  ...  This way we expand the applicability of three step method (2) under weak conditions.  ... 
doi:10.37256/cm.132020403 fatcat:23z6d4npazcmjfk2czarqsyywi

Ball convergence for combined three-step methods under generalized conditions in Banach space

Ioannis K. Argyros, Ramandeep Behl, Daniel Gonzalez, Sandile S. Motsa, Cameron University, Department of Mathematics Sciences, Lawton, OK 73505, USA e-mail:", "Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia e-mail:", "Universidad de Las Americas, Escuela de Ciencias Fisicas y Matematicas, Quito, 170125, Ecuador e-mail:", "University of KwaZulu-Natal, School of Mathematics, Statistics and Computer Sciences, Private Bag X01, Scottsville 3209, Pietermaritzburg, South Africa e-mail:"
2020 Studia Universitatis Babes-Bolyai Matematica  
We give a local convergence analysis for an eighth-order convergent method in order to approximate a locally unique solution of nonlinear equation for Banach space valued operators.  ...  Therefore, we not only expand the applicability of these methods but also provide the computable radius of convergence of these methods.  ...  → Y is a Fréchet-differentiable operator, X, Y are Banach spaces and D is a convex subset of X.  ... 
doi:10.24193/subbmath.2020.1.10 fatcat:m73uwcloxra2vhtt6wp2xng2dm

Inclusions in general spaces: Hoelder stability, solution schemes and Ekeland's principle

Bernd Kummer
2009 Journal of Mathematical Analysis and Applications  
We present two basic lemmas on exact and approximate solutions of inclusions and equations in general spaces.  ...  Our basic models are (multi-) functions on a complete metric space with images in a linear normed space.  ...  Acknowledgments The author is indebted to Diethard Klatte, Jan Heerda and Alexander Kruger for various helpful discussions and to the referees for constructive comments and hints concerning the subject of  ... 
doi:10.1016/j.jmaa.2009.04.060 fatcat:x3j3ps3jd5g3nen4ib24mqn45u

Mean-Field Learning: a Survey [article]

Hamidou Tembine, Raul Tempone, Pedro Vilanova
2012 arXiv   pre-print
Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the Banach-Picard iteration converges with geometrical convergence rate.  ...  When the best reply map is not a contraction, Ishikawa-based learning is proposed. The algorithm is shown to behave well for Lipschitz continuous and pseudo-contractive maps.  ...  Under feasibility condition, the algorithm generates an error as d(a t , a * ) ≤ ρ(M w ) t d(a 0 , a * ), which provides the convergence of the algorithm to a * .  ... 
arXiv:1210.4657v1 fatcat:63ofgy5vwfdt7j4kcw4za777wq

Asymptotic almost-equivalence of Lipschitz evolution systems in Banach spaces

Felipe Alvarez, Juan Peypouquet
2010 Nonlinear Analysis  
In particular, we establish convergence, ergodic convergence and almost-convergence of almost-orbits both for the weak and the strong topologies based on the behavior of the orbits.  ...  In this paper we introduce a notion of asymptotic almost-equivalence of two evolution systems and provide simple tests that guarantee that two evolution systems have the same qualitative asymptotic properties  ...  Banach spaces.  ... 
doi:10.1016/ fatcat:xzz4liizijacrkra5yafjdx6z4

A Moving Balls Approximation Method for a Class of Smooth Constrained Minimization Problems

Alfred Auslender, Ron Shefi, Marc Teboulle
2010 SIAM Journal on Optimization  
We introduce a new algorithm for a class of smooth constrained minimization problems which is an iterative scheme that generates a sequence of feasible points that approximates the constraints set by a  ...  Theoretical and computational properties of MBA and of some variant, in its primal and dual forms are studied, and convergence and global rate of convergence results are established for nonconvex and convex  ...  Let X be a Banach space and L a locally compact Hausdorff space.  ... 
doi:10.1137/090763317 fatcat:l5cjkksbwrardhmpagkno2jmz4

Convergence Criteria of Three Step Schemes for Solving Equations

Samundra Regmi, Christopher I. Argyros, Ioannis K. Argyros, Santhosh George
2021 Mathematics  
We develop a unified convergence analysis of three-step iterative schemes for solving nonlinear Banach space valued equations.  ...  So, the usage of them is restricted six or higher differentiable mappings. But in our paper only the first Frèchet derivative is utilized to show convergence. Consequently, the scheme is expanded.  ...  In order to extend the utilization of these schemes, we study the local convergence of scheme (2): in a Banach space, under generalized continuity conditions and using hypotheses only on the operators  ... 
doi:10.3390/math9233106 fatcat:eo7dnglcpnfshh3troeibdjm6u

Extended Local Convergence for High Order Schemes Under ω-Continuity Conditions

Gus Argyros, Michael Argyros, Ioannis K. Argyros, Santhosh George
2020 Contemporary Mathematics  
There is a plethora of schemes of the same convergence order for generating a sequence approximating a solution of an equation involving Banach space operators.  ...  But the set of convergence criteria is not the same in general. This makes the comparison between them challenging and only numerically.  ...  In particular, when X = Y = R i (i a natural number) Chun and Neta [1] presented a unified way of dealing with the local convergence of the three step IS given for x 0 ∈ D by y n = x n − αF'(x n ) −1  ... 
doi:10.37256/cm.152020709 fatcat:tmdjpqp4yncytamckxfjfuiutq

Ball Convergence for Combined Three-Step Methods Under Generalized Conditions in Banach Space

R. A. Alharbey, Ioannis K. Argyros, Ramandeep Behl
2019 Symmetry  
Finally, we consider a good mixture of numerical examples in order to demonstrate the applicability of our results in cases not covered before.  ...  That is why, we suggest higher-order iterative method to solve equations with Banach space valued operators.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/sym11081002 fatcat:dq2dpkz725cxrjbhvtsohz4v7u

Page 3760 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
These are, on one hand, that the above scheme is, under suitable hypotheses, well posed and provides a discrete function which converges uniformly in the seminorm induced by B to a strong solution of the  ...  2004e:34099 2004e:34099 34G25 35A35 35K65 35K90 65M06 Bassetti, Federico (I-PAVI; Pavia) Variable time-step discretization of degenerate evolution equations in Banach spaces. (English summary) Numer.  ... 

Implicit and explicit iterative algorithms for hierarchical variational inequality in uniformly smooth Banach spaces

Lu-Chuan Ceng, Yung-Yih Lur, Ching-Feng Wen
2017 Journal of Inequalities and Applications  
The purpose of this paper is to solve the hierarchical variational inequality with the constraint of a general system of variational inequalities in a uniformly convex and 2-uniformly smooth Banach space  ...  We introduce implicit and explicit iterative algorithms which converge strongly to a unique solution of the hierarchical variational inequality problem.  ...  solution of () and proved the weak convergence of the sequences generated by the proposed scheme.  ... 
doi:10.1186/s13660-017-1523-8 pmid:29051694 pmcid:PMC5628251 fatcat:xfiuycg6mbhztmsti3tucpeenq

The gradient flow structures of thermo-poro-visco-elastic processes in porous media [article]

Jakub Wiktor Both, Kundan Kumar, Jan Martin Nordbotten, Florin Adrian Radu
2019 arXiv   pre-print
For such, the energy decrease per iteration is quantified by applying abstract convergence theory only utilizing convexity and Lipschitz continuity properties of the problem -- a fairly simple but flexible  ...  In the first part, a modelling framework is introduced aiming for describing such processes as generalized gradient flows requiring choices of physical states, corresponding energies, dissipation potentials  ...  Acknowledgements This work is supported in part by the Research Council of Norway Project 250223. The authors also acknowledge the support from the University of Bergen.  ... 
arXiv:1907.03134v2 fatcat:3m4z4vkl4bhqbir3zg7bqrns6m
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