Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings by Jong Soo Jung

“…Certain different control conditions for viscosity iterative scheme are given and strong convergence of viscosity iterative scheme to a solution of a ceratin variational inequality is established.…”
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New Iterative Manner Involving Sunny Nonexpansive Retractions for Pseudocontractive Mappings by Yaqin Zheng, Jinwei Shi

“…Consequently, we show that the suggested algorithm converges strongly to a fixed point of the pseudocontractive mapping which also solves some variational inequality.…”
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Projection Algorithms for Variational Inclusions by Youli Yu, Pei-Xia Yang, Khalida Inayat Noor

“…Furthermore, we prove that the proposed iterative algorithm converges strongly to a solution of the variational inclusion problem which also solves some variational inequality.…”
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Strong Convergence Theorems for Common Fixed Points of an Infinite Family of Asymptotically Nonexpansive Mappings by Yuanheng Wang

“…Under some appropriate conditions, we prove that the iterative sequences {xn} converge strongly to a common fixed point of the mappings Tii=1∞, which is also a solution of a variational inequality. Our results extend and improve some recent results of other authors.…”
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Upper Semicontinuity of Solution Mappings to Parametric Generalized Vector Quasiequilibrium Problems by Shu-qiang Shan, Yu Han, Nan-jing Huang

“…As applications, we obtain the upper semicontinuity of solution mappings to several problems, such as parametric optimization problem, parametric saddle point problem, parametric Nash equilibria problem, parametric variational inequality, and parametric equilibrium problem.…”
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Hybrid Projection Algorithm for Two Countable Families of Hemirelatively Nonexpansive Mappings and Applications by Zi-Ming Wang, Poom Kumam

“…As applications, convex feasibility problems, equilibrium problems, variational inequality problems, and zeros of maximal monotone operators are studied.…”
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Regularity for Variational Evolution Integrodifferential Inequalities by Yong Han Kang, Jin-Mun Jeong

“…We deal with the regularity for solutions of nonlinear functional integrodifferential equations governed by the variational inequality in a Hilbert space. Moreover, by using the simplest definition of interpolation spaces and the known regularity result, we also prove that the solution mapping from the set of initial and forcing data to the state space of solutions is continuous, which very often arises in application. …”
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Weak Convergence Theorems for Strictly Pseudocontractive Mappings and Generalized Mixed Equilibrium Problems by Jong Soo Jung

“…We introduce a new iterative method for finding a common element of the set of fixed points of a strictly pseudocontractive mapping, the set of solutions of a generalized mixed equilibrium problem, and the set of solutions of a variational inequality problem for an inverse-strongly-monotone mapping in Hilbert spaces and then show that the sequence generated by the proposed iterative scheme converges weakly to a common element of the above three sets under suitable control conditions. …”
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Viscosity Approximation Methods and Strong Convergence Theorems for the Fixed Point of Pseudocontractive and Monotone Mappings in Banach Spaces by Yan Tang

“…And the common element is the unique solution of certain variational inequality. The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings.…”
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The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces by Rabian Wangkeeree

“…We introduce two general hybrid iterative approximation methods (one implicit and one explicit) for finding a fixed point of a nonexpansive mapping which solving the variational inequality generated by two strongly positive bounded linear operators. …”
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Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces by Prasit Cholamjiak, Suthep Suantai

“…In addition, the results obtained in this paper can be applied to a system of variational inequality problems and to a system of convex minimization problems in a Banach space.…”
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Strong Convergence to Solutions of Generalized Mixed Equilibrium Problems with Applications by Prasit Cholamjiak, Suthep Suantai, Yeol Je Cho

“…As applications, we apply our main result to mixed equilibrium, generalized equilibrium, and mixed variational inequality problems in Banach spaces. Finally, examples and numerical results are also given.…”
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A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems by Yekini Shehu

“…Using this result, we discuss strong convergence theorem concerning variational inequality and convex minimization problems in Banach spaces. …”
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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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