Iterative Methods of Weak and Strong Convergence Theorems for the Split Common Solution of the Feasibility Problems, Generalized Equilibrium Problems, and Fixed Point Problems by Shahram Rezapour, Yuanheng Wang, Seyyed Hasan Zakeri

“…As applications of our three main theorems, when the mappings and their domains take different types of cases, we can obtain nine iterative approximation theorems and corollas on fixed points, variational inequality solutions, and equilibrium points.…”
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A New Iterative Method for Equilibrium Problems and Fixed Point Problems by Abdul Latif, Mohammad Eslamian

“…We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. …”
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A Quasi-Variational Approach for the Dynamic Oligopolistic Market Equilibrium Problem by Annamaria Barbagallo, Paolo Mauro

“…As a consequence, we introduce the generalized dynamic Cournot-Nash principle in the elastic case and prove the equivalence between this equilibrium definition and a suitable evolutionary quasi-variational inequality. For completeness we make the analysis of existence, regularity, and sensitivity of the solution. …”
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Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces by Chin-Tzong Pang, Eskandar Naraghirad

“…We prove strong convergence theorems for the sequences produced by the methods and approximate a common fixed point of a countable family of nonexpansive mappings which solves uniquely the corresponding variational inequality. Furthermore, we apply our results for finding a zero of an accretive operator. …”
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Algorithmic Approach to a Minimization Problem by Yonghong Yao, Shin Min Kang, Yeong-Cheng Liou, Zhitao Wu

“…We first construct an implicit algorithm for solving the minimization problem minx∈Ω∥x∥ , where Ω is the intersection set of the solution set of some equilibrium problem, the fixed points set of a nonexpansive mapping, and the solution set of some variational inequality. Further, we suggest an explicit algorithm by discretizing this implicit algorithm. …”
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Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces by Si-Huan Li, Qiang Wang, Shu Xu, Jun-Xiang Wang

“…As applications, some necessary optimality conditions and sufficient optimality conditions for local sharp efficient solutions of a vector optimization problem with an abstract constraint and a vector variational inequality are obtained, respectively.…”
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A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces by Pongsakorn Sunthrayuth, Poom Kumam

“…As applications, finding a common solution for a system of variational inequality problems and minimization problems is given.…”
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A New Hybrid Algorithm for a Pair of Quasi-𝜙-Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces by Jinhua Zhu, Shih-Sen Chang

“…The purpose of this paper is, by using a new hybrid method, to prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for a variational inequality problem, and the set of common fixed points for a pair of quasi-𝜙-asymptotically nonexpansive mappings. …”
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A Mixed Traffic Assignment Problem and Its Upper Bound of Efficiency Loss by Xiao-Jun Yu, Jiancheng Long

“…A variational inequality (VI) formulation of a mixed traffic assignment problem associated with user equilibrium (UE) player and altruistic players (UE-AP) is developed. …”
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Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions by Yan Wang, Aimin Song, Cheng-De Zheng, Enmin Feng

“…By a dynamic programming approach, we give a verification theorem in terms of variational inequality-Hamilton-Jacobi-Bellman (VIHJB) equations for the solutions of the game. …”
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Dynamic Combined-Mode Traffic Network Model considering Transfer Behaviors by ShuGuang Li, QingHua Zhou

“…We present an integrated variational inequality formulation to capture the complex traveler choice behaviors such as departure time choices, transfer point, and route choices. …”
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Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems by Lu-Chuan Ceng, Ching-Feng Wen

“…It is proven that three sequences generated by this algorithm converge strongly to the unique solution of some variational inequality, which is also a common element of the set of solutions of a constrained convex minimization problem, the set of solutions of a generalized mixed equilibrium problem, and the set of fixed points of a strict pseudocontraction in a real Hilbert space.…”
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The Nonsteady Boussinesq System with Mixed Boundary Conditions including Conditions of Friction Type by Tujin Kim

“…The formulations consist of a variational inequality for velocity due to the boundary conditions of friction type and a variational equation for temperature. …”
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A Novel System and Iterative Schemes for Generalized Variational Inclusion Problems and its Approximation Solvability by Mohd Sarfaraz, Md. Kalimuddin Ahmad

“…The variational inclusion problems are the generalizations of the variational inequality problems. First, it was noted by Hasounni and Moudafi in 1994. …”
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Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces by Yali Li, Jianjun Liu, Lei Deng

“…We prove that the following implicit and modified implicit viscosity iterative schemes {xn} defined by xn=αnf(xn)+(1−αn)T(tn)xn and xn=αnyn+(1−αn)T(tn)xn, yn=βnf(xn−1)+(1−βn)xn−1 strongly converge to p∈F as n→∞ and p is the unique solution to the following variational inequality: 〈f(p)−p,j(y−p)〉≤0 for all y∈F.…”
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A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems wit... by Uamporn Witthayarat, Thanyarat Jitpeera, Poom Kumam

“…The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. …”
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Bounding the Inefficiency of the Multiclass, Multicriteria C-Logit Stochastic User Equilibrium in a Transportation Network by Lekai Yuan, Xi Zhang, Chaofeng Shi

“…To find efficiency loss upper bounds of the multiclass CL-SUE, two equivalent variational inequalities for the multiclass CL-SUE model, i.e., time-based variational inequality (VI) and monetary-based VI, are formulated. …”
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A Reliability-Based Network Equilibrium Model with Adaptive Risk-Averse Travelers by Lei Zhao, Hongzhi Guan, Junze Zhu, Yunfeng Wei

“…Moreover, its equivalent variational inequality (VI) problem is formulated and a route-based algorithm is used to solve the proposed model. …”
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The Role of Initial Credit Distribution Scheme in Managing Network Mobility and Maximizing Reserve Capacity: Considering Traveler’s Cognitive Illusion by Fei Han, Lin Cheng

“…To comprehensively reveal the impacts of ICDS on UE solution, four different types of ICDS are introduced and analyzed in a unified variational inequality (VI) modeling framework. The uniqueness of the UE link flow and market equilibrium (ME) credit price is also investigated. …”
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Multiple Equilibrium Behaviors considering Human Exposure to Vehicular Emissions by Zhanbo Sun, Yu Tan, Rui Ma, Xia Yang, Jie Zhang

“…The multiple equilibrium problems are further converted into variational inequality (VI) problems and they are solved using a method of successive average- (MSA-) based diagonalization method. …”
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