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On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications

Teng-fei Li, Heng-you Lan
2019 Journal of Function Spaces  
the new Picard-Mann iteration process with mixed errors for the implicit midpoint rule of nonexpansive mappings is brand new and more effective than other related iterative processes.  ...  The purpose of this paper is to introduce and study a class of new Picard-Mann iteration processes with mixed errors for the implicit midpoint rules, which is different from existing methods in the literature  ...  Acknowledgments This work was partially supported by Sichuan Science and Technology Program (2019YJ0541) and the Scientific Research Project of Sichuan University of Science & Engineering (2013PY07).  ... 
doi:10.1155/2019/4042965 fatcat:xhav4vwqbfgvlmg3zefeivtv3y

Fixed point theorems for Kannan type mappings with applications to split feasibility and variational inequality problems [article]

Vasile Berinde, Mădălina Păcurar
2019 arXiv   pre-print
As applications of our main fixed point theorems, we present two Kransnoselskij projection type algorithms for solving split feasibility problems and variational inequality problems in the class of enriched  ...  We study the set of fixed points and prove a convergence theorem for Kransnoselskij iteration used to approximate fixed points of enriched Kannan mappings in Banach spaces.  ...  For this mapping, as shown in the previous section, Picard iteration does not converge, in general.  ... 
arXiv:1909.02379v1 fatcat:kb6jmlm64zdhrer43d3r5wqaja

Krasnoselskij-type algorithms for variational inequality problems and fixed point problems in Banach spaces [article]

Vasile Berinde, Madalina Pacurar
2021 arXiv   pre-print
An application of the strong convergence theorems to solving a variational inequality is also presented.  ...  Existence and uniqueness as well as the iterative approximation of fixed points of enriched almost contractions in Banach spaces are studied.  ...  Acknowledgments The first author's research was supported by the Department of Mathematics and Computer Science, Technical University of Cluj-Napoca, North University Centre at Baia Mare, through the Internal  ... 
arXiv:2103.10289v1 fatcat:ea2enss7vjcmlaxcdxmtlm3ll4

Iterative Methods and Applications 2014

Giuseppe Marino, Filomena Cianciaruso, Claudio H. Morales, Luigi Muglia, D. R. Sahu
2015 Journal of Applied Mathematics  
Zhang et al. introduce a new iterative scheme for finding a common fixed point of two countable families of multivalued quasi-nonexpansive mappings and prove a weak convergence theorem under the suitable  ...  of variational inequalities problems or split feasibility problems and applications, (iv) optimization problems and their algorithmic approaches, (v) methods for the global continuation of fixed point  ...  Acknowledgments The editors would like to thank the authors for their interesting contributions, as well as the Staff and the Editorial Office of the Journal for their valuable support.  ... 
doi:10.1155/2015/207976 fatcat:iahrwjmrujd63ozjakojc2zia4

Iterative Methods and Applications

Giuseppe Marino, Filomena Cianciaruso, Luigi Muglia, Claudio H. Morales, Daya Ram Sahu
2014 Journal of Applied Mathematics  
, the approximation of fixed points of nonlinear operators, of zeros of nonlinear operators, and the approximation of solutions of variational inequalities.  ...  An important branch of nonlinear analysis theory, applied in the study of nonlinear phenomena in engineering, physics, and life sciences, is related to the existence of fixed points of nonlinear mappings  ...  Acknowledgment The editors would like to thank the authors for their interesting contributions. Giuseppe Marino Filomena Cianciaruso Luigi Muglia Claudio H. Morales Daya Ram Sahu  ... 
doi:10.1155/2014/827064 fatcat:p43ncbk2yfbotcq2w23i4ln66q

New approximation methods for solving elliptic boundary value problems via Picard-Mann iterative processes with mixed errors

Teng-fei Li, Heng-you Lan
2017 Boundary Value Problems  
In this paper, we introduce and study a class of new Picard-Mann iterative methods with mixed errors for common fixed points of two different nonexpansive and contraction operators.  ...  the Picard iterative process, Mann iterative process, Picard-Mann iterative process due to Khan and other related iterative processes.  ...  Acknowledgements We would like to thank the editors and referees for their valuable comments and suggestions to improve our paper.  ... 
doi:10.1186/s13661-017-0914-6 fatcat:pd7ah7qfxzginib34scjy7x3oi

On the Strong Convergence Theorem of Noor Iterative Scheme in the Class of Zamfirescu Operators

Mohammad Asaduzzaman
2013 Pure and Applied Mathematics Journal  
Our results is extension and generalization of the recent results of B.  ...  In this paper, we establish the strong convergence theorem of Noor iterative scheme for the class of Zamfirescu operators in arbitrary Banach spaces.  ...  Strodiot [27] studied the convergence analysis of three-step iteration scheme of Glowinski and Le Tallec [26] and applied this scheme to obtain new splitting-type algorithms for solving variation inequalities  ... 
doi:10.11648/j.pamj.20130204.11 fatcat:ckh672ssbvh3dgwe3aqcjsw2b4

Coupled solutions for a bivariate weakly nonexpansive operator by iterations

Vasile Berinde, Abdul Khan, Madalina Păcurar
2014 Fixed Point Theory and Applications  
We prove weak and strong convergence theorems for a double Krasnoselskij-type iterative method to approximate coupled solutions of a bivariate nonexpansive operator F : C × C → C, where C is a nonempty  ...  closed and convex subset of a Hilbert space.  ...  a few (non-fatal) errors in the proofs.  ... 
doi:10.1186/1687-1812-2014-149 fatcat:bgnnwg4zmfgu5nrrenfco4c7b4

Convergence Analysis of Parallel S-Iteration Process for System of Generalized Variational Inequalities

D. R. Sahu, Shin Min Kang, Ajeet Kumar
2017 Journal of Function Spaces  
We consider a new system of generalized variational inequalities (SGVI) defined on two closed convex subsets of a real Hilbert space.  ...  To find the solution of considered SGVI, a parallel Mann iteration process and a parallel S-iteration process have been proposed and the strong convergence of the sequences generated by these parallel  ...  Acknowledgments The third author is supported by the Council of Scientific and Industrial Research (CSIR), New Delhi, India, through Grant 09/013(0584)/2015-EMR-I.  ... 
doi:10.1155/2017/5847096 fatcat:5srrfhijibhvvobzpz76mhwqmq

Coupled solutions for a bivariate weakly nonexpansive operator by iterations [article]

V. Berinde, A. R. Khan, M. Pacurar
2014 arXiv   pre-print
We prove weak and strong convergence theorems for a double Krasnoselskij type iterative method to approximate coupled solutions of a bivariate nonexpansive operator F : C x C --> C, where C is a nonempty  ...  closed and convex subset of a Hilbert space.  ...  He gratefully thanks the host for kind hospitality and excellent work facilities offered.  ... 
arXiv:1402.5128v1 fatcat:3x637xpu5fahdoe5en2hcnuczi

New Iterative Algorithm for Solving Constrained Convex Minimization Problem and Split Feasibility Problem

Austine Efut Ofem, Unwana Effiong Udofia, Donatus Ikechi Igbokwe
2021 European Journal of Mathematical Analysis  
The purpose of this paper is to introduce a new iterative algorithm to approximate the fixed points of almost contraction mappings and generalized α-nonexpansive mappings.  ...  mappings and generalized α-nonexpansive mappings.  ...  than M iterative algorithm and some other well known existing iterative algorithms in the literature for almost contraction mapping and generalized α-nonexpansive mappings.  ... 
doi:10.28924/ada/ma.1.106 doaj:9decb33fa98f40559a8b3bb2f835fb9c fatcat:uzcejteysrbhtp66aecshdlslm

Page 1936 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
Moreover, the iteration method, suitably combined, by a Staircase technique, with approximations of P by a sequence of nonexpansive mappings P,, and with regularization, generates a sequence that converges  ...  From the summary: “Let C be a nonempty closed convex subset of the Hilbert space # and P be a nonexpansive mapping from C into C.  ... 

A Modified Krasnosel'skiǐ–Mann Iterative Algorithm for Approximating Fixed Points of Enriched Nonexpansive Mappings

Vasile Berinde
2022 Symmetry  
For approximating the fixed points of enriched nonexpansive mappings in Hilbert spaces, we consider a modified Krasnosel'skiǐ–Mann algorithm for which we prove a strong convergence theorem.  ...  Based on the numerical experiments reported in the paper we conclude that, for the class of enriched nonexpansive mappings, it is more convenient to work with the simple Krasnosel'skiǐ fixed point algorithm  ...  point problems for appropriate nonexpansive mappings: convex feasibility problems, convex optimization problems, monotone variational inequalities, image recovery, signal processing, and so on.  ... 
doi:10.3390/sym14010123 fatcat:adswstl7z5eevobmf7rec6sqn4

Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems

Bing Tan, Shanshan Xu, Songxiao Li
2020 Mathematics  
Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory.  ...  In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm  ...  Acknowledgments: We greatly appreciate the reviewers for their helpful comments and suggestions. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math8020236 fatcat:foroi2ujdngwhadkujdyz3wxgi

Efficient First Order Methods for Linear Composite Regularizers [article]

Andreas Argyriou, Charles A. Micchelli, Massimiliano Pontil, Lixin Shen, Yuesheng Xu
2011 arXiv   pre-print
Our approach builds on a recent line of research on optimal first order optimization methods and uses fixed point iterations for numerically computing the proximity operator.  ...  This setting includes Group Lasso methods, the Fused Lasso and other total variation methods, multi-task learning methods and many more.  ...  Acknowledgements We wish to thank Luca Baldassarre and Silvia Villa for useful discussions. This work was sup-  ... 
arXiv:1104.1436v1 fatcat:iyl4zuclqrcrdohmnzt4nnqukq
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