A New Gap Function for Vector Variational Inequalities with an Application by Hui-qiang Ma, Nan-jing Huang, Meng Wu, Donal O'Regan

“…We consider a vector variational inequality in a finite-dimensional space. A new gap function is proposed, and an equivalent optimization problem for the vector variational inequality is also provided. …”
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Hybrid Steepest-Descent Methods for Triple Hierarchical Variational Inequalities by L. C. Ceng, A. Latif, C. F. Wen, A. E. Al-Mazrooei

“…We prove that, under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings, the solution set of finitely many generalized mixed equilibrium problems (GMEPs), the solution set of finitely many variational inclusions, and the solution set of general system of variational inequalities (GSVI), which is just a unique solution of a triple hierarchical variational inequality (THVI) in a real Hilbert space. …”
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Algorithms for a System of General Variational Inequalities in Banach Spaces by Jin-Hua Zhu, Shih-Sen Chang, Min Liu

“…The purpose of this paper is using Korpelevich's extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. …”
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MULTI-VALUED TIKHONOV TRAJECTORIES OF GENERAL AFFINE VARIATIONAL INEQUALITIES by Nguyễn Thị Thu Hương, Phan Duy Khánh, Nguyễn Đông Yên

Subjects: “…Affine variational inequality…”
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A New System of Multivalued Mixed Variational Inequality Problem by Xi Li, Xue-song Li

“…We consider a new system of multivalued mixed variational inequality problem, which includes some known systems of variational inequalities as special cases. …”
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Topological degree and application to a parabolic variational inequality problem by A. Addou, B. Mermri

“…By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.…”
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Certain remarks on a class of evolution quasi-variational inequalities by A. H. Siddiqi, Pammy Manchanda

Subjects: “…Evolution quasi-variational inequalities…”
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New results on system of variational inequalities and fixed point theorem by Ayache Benhadid, Mahmoud Brahimi

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Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities by Jong Soo Jung

“…Such a point is also a solution of a variational inequality defined on the set of fixed points. …”
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Finite element estimates for a class of nonlinear variational inequalities by Muhammad Aslam Noor

“…It is well known that a wide class of obstacle and unilateral problems arising in pure and applied sciences can be studied in a general and unifield framework of variational inequalities. In this paper, we derive the error estimates for the finite element approximate solution for a class of highly nonlinear variational inequalities encountered in the field of elasticity and glaciology in terms of W1,p(Ω) and Lp(Ω)-norms. …”
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Numerical and Analytical Methods for Variational Inequalities and Related Problems with Applications by Zhenyu Huang, Ram N. Mohapatra, Muhammad Aslam Noor, Hong-Kun Xu, Qingzhi Yang

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Ordered Variational Inequalities and Ordered Complementarity Problems in Banach Lattices by Jinlu Li, Ching-Feng Wen

“…We introduce the concepts of ordered variational inequalities and ordered complementarity problems with both domain and range in Banach lattices. …”
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A Class of Fuzzy Variational Inequality Based on Monotonicity of Fuzzy Mappings by Zezhong Wu, Jiuping Xu

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Bregman f-Projection Operator with Applications to Variational Inequalities in Banach Spaces by Chin-Tzong Pang, Eskandar Naraghirad, Ching-Feng Wen

“…The existence of a solution for a class of variational inequalities in Banach spaces is presented.…”
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Nonlinear variational inequalities on reflexive Banach spaces and topological vector spaces by Zeqing Liu, Jeong Sheok Ume, Shin Min Kang

“…The purpose of this paper is to introduce and study a class of nonlinear variational inequalities in reflexive Banach spaces and topological vector spaces. …”
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General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities by Nopparat Wairojjana, Poom Kumam

“…Under a suitable different parameter, we obtain strong convergence theorems by using the projection method which solves the variational inequality 〈(A-γf)x̃+τ(I-S)x̃,x-x̃〉≥0 for x∈F(T), where τ∈[0,∞). …”
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Some New Classes of Extended General Mixed Quasi-Variational Inequalities by Muhammad Aslam Noor, Khalida Inayat Noor

“…We consider and study a new class of variational inequality, which is called the extended general mixed quas-variational inequality. …”
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An Optimal Control Problem Governed by a Kirchhoff-Type Variational Inequality by Chengfu Wang, Pengcheng Wu, Yuying Zhou

“…This paper is concerned with an optimal control problem governed by a Kirchhoff-type variational inequality. The existence of multiplicity solutions for the Kirchhoff-type variational inequality is established by using some nonlinear analysis techniques and the variational method, and the existence results of an optimal control for the optimal control problem governed by a Kirchhoff-type variational inequality are derived.…”
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A New Iterative Algorithm for General Variational Inequality Problem with Applications by Aysha Khan, M. Akram, M. Dilshad, J. Shafi

“…This study aims at investigation of a generalized variational inequality problem. We initiate a new iterative algorithm and examine its convergence analysis. …”
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Viscosity Methods of Asymptotically Pseudocontractive and Asymptotically Nonexpansive Mappings for Variational Inequalities by Xionghua Wu, Yeong-Cheng Liou, Zhitao Wu, Pei-Xia Yang

“…If 𝑇 be a continuous asymptotically pseudocontractive self-mapping of a nonempty bounded closed convex subset 𝐾 of a real reflexive Banach space with a uniformly Gateaux differentiable norm, under suitable conditions on the sequence {𝑡𝑛}, we show the existence of a sequence {𝑥𝑛}𝑛 satisfying the relation 𝑥𝑛=(1−𝑡𝑛/𝑘𝑛)𝑓(𝑥𝑛)+(𝑡𝑛/𝑘𝑛)𝑇𝑛𝑥𝑛 and prove that {𝑥𝑛} converges strongly to the fixed point of 𝑇, which solves some variational inequality provided 𝑇 is uniformly asymptotically regular. …”
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