Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities by Muhammad Aslam Noor, Khalida Inayat Noor, Saira Zainab

“…We introduce and consider a new class of equilibrium problems and variational inequalities involving bifunction, which is called the nonconvex bifunction equilibrium variational inequality. …”
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Forward-backward resolvent splitting methods for general mixed variational inequalities by Muhammad Aslam Noor, Muzaffar Akhter, Khalida Inayat Noor

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Novel Algorithms for Solving a System of Absolute Value Variational Inequalities by Safeera Batool, Muhammad Aslam Noor, Riaz Ahmad, Ilyas Khan, Mulugeta Andualem

“…The goal of this paper is to study a new system of a class of variational inequalities termed as absolute value variational inequalities. …”
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A Self-Adaptive Extragradient Algorithm for Solving Quasimonotone Variational Inequalities by Li-Jun Zhu, Tzu-Chien Yin

“…This article aims to research iterative schemes for searching a solution of a quasimonotone variational inequality in a Hilbert space. For solving this quasimonotone variational inequality, we propose an iterative procedure which combines a self-adaptive rule and the extragradient algorithm. …”
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NONLINEAR PERTURBATIONS OF POLYHEDRAL NORMAL CONE MAPPINGS AND AFFINE VARIATIONAL INEQUALITIES by Nguyễn Thành Quí

“…On the basis, new results on solution stability of parametric affine variational inequalities under nonlinear perturbations are derived.…”
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Convergence Analysis of Parallel S-Iteration Process for System of Generalized Variational Inequalities by D. R. Sahu, Shin Min Kang, Ajeet Kumar

“…We consider a new system of generalized variational inequalities (SGVI) defined on two closed convex subsets of a real Hilbert space. …”
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Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces by Lu-Chuan Ceng, Ching-Feng Wen

“…We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi (1995, 1996) for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. …”
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On the Hadamard Well-Posedness of Generalized Mixed Variational Inequalities in Banach Spaces by Lu-Chuan Ceng, Yeong-Cheng Liou, Ching-Feng Wen, Hui-Ying Hu, Long He, Yun-Ling Cui

“…We introduce a new concept of Hadamard well-posedness of a generalized mixed variational inequality in a Banach space. The relations between the Levitin–Polyak well-posedness and Hadamard well-posedness for a generalized mixed variational inequality are studied. …”
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Fixed Points Approximation and Solutions of Some Equilibrium and Variational Inequalities Problems by Bashir Ali

“…We prove a new strong convergence theorem for an element in the intersection of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of some variational inequality problems, and the set of solutions of some equilibrium problems using a new iterative scheme. …”
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Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces by Panisa Lohawech, Anchalee Kaewcharoen, Ali Farajzadeh

“…In this paper, we establish an iterative algorithm by combining Yamada’s hybrid steepest descent method and Wang’s algorithm for finding the common solutions of variational inequality problems and split feasibility problems. …”
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Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials by Dumitru Motreanu, Mircea Sofonea

“…We consider a class of evolutionary variational inequalities arising in quasistatic frictional contact problems for linear elastic materials. …”
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Generalized Complementarity Problem with Three Classes of Generalized Variational Inequalities Involving ⊕ Operation by Rais Ahmad, Iqbal Ahmad, Zahoor Ahmad Rather, Yuanheng Wang

“…In this study, we introduce and study a generalized complementarity problem involving XOR operation and three classes of generalized variational inequalities involving XOR operation. Under certain appropriate conditions, we establish equivalence between them. …”
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Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups by Li-Jun Zhu

“…The purpose of the present paper is to study the hierarchical constrained variational inequalities of finding a point x* such that x*∈Ω,〈(A-γf)x*-(I-B)Sx*,x-x*〉≥0,  ∀x∈Ω, where Ω is the set of the solutions of the following variational inequality: x*∈Ϝ,〈(A-S)x*,x-x*〉≥0,  ∀x∈Ϝ, where A,B are two strongly positive bounded linear operators, f is a ρ-contraction, S is a nonexpansive mapping, and Ϝ is the fixed points set of a nonexpansive semigroup {T(s)}s≥0. …”
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On the solvability of a variational inequality problem and application to a problem of two membranes by A. Addou, E. B. Mermri

“…The purpose of this work is to give a continuous convex function, for which we can characterize the subdifferential, in order to reformulate a variational inequality problem: find u=(u1,u2)∈K such that for all v=(v1,v2)∈K, ∫Ω∇u1∇(v1−u1)+∫Ω∇u2∇(v2−u2)+(f,v−u)≥0 as a system of independent equations, where f belongs to L2(Ω)×L2(Ω) and K={v∈H01(Ω)×H01(Ω):v1≥v2  a.e. in Ω}.…”
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Implicit and Explicit Iterative Methods for Systems of Variational Inequalities and Zeros of Accretive Operators by Lu-Chuan Ceng, Saleh Abdullah Al-Mezel, Qamrul Hasan Ansari

“…Based on Korpelevich's extragradient method, hybrid steepest-descent method, and viscosity approximation method, we propose implicit and explicit iterative schemes for computing a common element of the solution set of a system of variational inequalities and the set of zeros of an accretive operator, which is also a unique solution of a variational inequality. …”
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Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities by M. Akram, Aysha Khan, M. Dilshad

“…In this article, we consider and study a system of generalized set-valued variational inequalities involving relaxed cocoercive mappings in Hilbert spaces. …”
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Iterative Algorithms for Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators by Caiping Yang, Songnian He

“…He and Xu proved that this variational inequality has a unique solution and devised iterative algorithms to approximate this solution (see He and Xu, 2009). …”
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Hybrid Extragradient Iterative Algorithms for Variational Inequalities, Variational Inclusions, and Fixed-Point Problems by Lu-Chuan Ceng, Ching-Feng Wen

“…We investigate the problem of finding a common solution of a general system of variational inequalities, a variational inclusion, and a fixed-point problem of a strictly pseudocontractive mapping in a real Hilbert space. …”
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A Self-Adaptive Technique for Solving Variational Inequalities: A New Approach to the Problem by Muhammad Bux, Saleem Ullah, Muhammad Shoaib Arif, Kamaleldin Abodayeh

“…Variational inequalities are considered the most significant field in applied mathematics and optimization because of their massive and vast applications. …”
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A New Implementable Prediction-Correction Method for Monotone Variational Inequalities with Separable Structure by Feng Ma, Mingfang Ni, Zhanke Yu

“…The monotone variational inequalities capture various concrete applications arising in many areas. …”
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