New approximation schemes for general variational inequalities

By Muhammad Aslam Noor. 2000

933 citations recorded by the source corpus.

In this paper, we suggest and consider a class of new three-step approximation schemes for general variational inequalities. Our results include Ishikawa and Mann iterations as special cases. We also study the convergence criteria of these schemes.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/8553e5575452fb85e9542fdcc3eacf60ed16baa2

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In Civil and Structural Engineering

In Computational Theory and Mathematics

Citations in the corpus

Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings (2006, methodology): “In 2000, Noor [10] introduced a three-step iterative scheme and study the approximate solutions of variational inclusion”
A PICARD-S HYBRID TYPE ITERATION METHOD FOR SOLVING A DIFFERENTIAL EQUATION WITH RETARDED ARGUMENT (2014, methodology): “The following tables 1-2-3 show that Picard-S iteration method (1.14) converges faster than all Picard (1.3), Mann (1.5), Ishikawa (1.6), Noor (1.7), SP (1.8), S (1.9) , CR (1.10), Normal-S [39], S* [19] and Two-Step Mann [45] iteration methods including a new three-step iteration method due to Abba”
Data dependence results of new multi-step and S-iterative schemes for contractive-like operators (2012, methodology): “e are many contractive mappings and iteration schemes that have been introduced and developed by several authors to serve various purposes in the literature of this highly active research area, viz., [2, 39, 28, 17, 3, 33, 38, 23, 4, 40, 10, 27], among others. Whether an iteration method used in any”
Mixed equilibrium problems and optimization problems (2009, background): “In this direction, several authors have introduced some iterative schemes for finding a common element of a set of the solutions of the equilibrium problems and a set of the fixed points of finitely many nonexpansive mappings, see [6,8,11– 17,30,32–45] and the references therein.”
Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process (2018, methodology): “In [4], the authors claimed that CR iteration process is equivalent to and faster than Picard, Mann, Ishikawa, Agarwal, Noor and SP iterative processes for quasi-contractive operators in Banach spaces.”
Projection algorithms for solving a system of general variational inequalities (2009, methodology): “For the applications and numerical methods, see [10,13–16,22–24] and the references therein.”
New Trends in General Variational Inequalities (2020, methodology): “This result is due to Noor [110, 122].”
FIXED POINT THEOREMS FOR GENERALIZED WEAKLY CONTRACTIVE MAPPINGS (2009, methodology): “Mann (cf. [19]) introduced a one-step iterative scheme, Isikawa (cf. [15]) introduced a two-step iterative scheme, and Noor (cf. [21]) introduced a three-step iterative scheme.”
Some developments in general variational inequalities (2004, methodology): “It is well known that a substantial number of numerical methods can be obtained as special cases from this technique, see [13,25,80,83, 87,98,103,112,150] and the references therein.”
A new iteration scheme for approximating fixed points of nonexpansive mappings (2016, neutral): “Step Picard Mann Ishikawa Noor Agarwal Abbas New iter.”
Three-step iterations for nonlinear accretive operator equations (2002, methodology): “For the applications of the splitting and decomposition methods, see [1,5,6,13–15] and the references therein.”
Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces (2010, methodology): “For the physical formulation, applications, numerical methods and other aspects of the variational inequalities, see [17–28] and the references therein.”
New extragradient-type methods for general variational inequalities (2003, neutral): “Keywords:Variational inequalities; Wiener–Hopf equations; Extragradient-type methods; Fixed-point; Convergence”