Some developments in general variational inequalities

By Muhammad Aslam Noor. Applied Mathematics and Computation, 2004

606 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c1535d4418e126af335fcfe886cfe0776b4e4cda

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces (2008, methodology): “The three-step schemes are natural generalization of the splitting methods to solve partial differential equations (inclusions); for details, see, Noor [14–16].”
On viscosity iterative methods for variational inequalities (2007, methodology): “Several numerical methods have been developed for solving variational inequalities and related optimization problems, see [1] and the references therein.”
Perturbed projections and subgradient projections for the multiple-sets split feasibility problem (2007, background): “Such a list includes, among many oth-Y ers, the works of Crombez [18,19], the connection with variational inequalities, see, e.g., Aslam Noor [21], Yamada’s [27] which is motivated by real-world problems of signal processing, and the many contributions of Bauschke and Combettes, see, e.g.,…”
Invex equilibrium problems (2005, methodology): “For the recent applications, numericals methods and formulations of variational inequalities, variational-like inequalities and equilibrium problems, see [1–41] and the references therein.”
Stable pseudomonotone variational inequality in reflexive Banach spaces (2007, result): “[11–14] studied the stability of variational inequalities and of quasivariational inequalities under some assumptions different from those of the main results in this paper.”
Projection algorithms for solving a system of general variational inequalities (2009, methodology): “In brief, the field of iterative methods is vast; see [1–28, 30] and the references therein.”
Outer approximation methods for solving variational inequalities in Hilbert space (2017, background): “In the last decades VIs have been extensively studied by many authors; see, for example, Facchinei’s and Pang’s two-volume book [27], the review papers by Xiu and Zhang [43], and Noor [3], as well as a recent one by Chugh and Rani [23].”
On interval-valued nonlinear programming problems (2008, background): “The details of this topic may refer to Noor [8,9].”
A new inertial double-projection method for solving variational inequalities (2019, background): “Our results can be extended in many promising directions, such as multivalued variational inequality [20], VIs combined with fixed point problems [10], system of VIs and mixed equilibrium problem [26], general VIs [35], strong convergence in Hilbert spaces as well as extensions to Banach spaces [9,3”