Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings by Yongfu Su

“…Meanwhile, a approximate iteration algorithm is presented which is used to calculate the fixed point of nonexpansive mapping and solution of variational inequality, the error estimate is also given. …”
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Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces by Luo Yi Shi, Ru Dong Chen

“…It is shown that under certain appropriate conditions on αn,{xn} converge strongly to a fixed point of T which solves some variational inequality.…”
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Algorithmic Approach to the Split Problems by Ming Ma

“…This paper deals with design algorithms for the split variational inequality and equilibrium problems. Strong convergence theorems are demonstrated.…”
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Fixed Point of Strong Duality Pseudocontractive Mappings and Applications by Baowei Liu

“…The purpose of this paper is to introduce the definition of α-strong duality pseudocontractive mappings and to study its fixed point problem and applications for operator equation and variational inequality problems.…”
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Damped Algorithms for the Split Fixed Point and Equilibrium Problems by Li-Jun Zhu, Minglun Ren

“…The main purpose of this paper is to study the split fixed point and equilibrium problems which includes fixed point problems, equilibrium problems, and variational inequality problems as special cases. A damped algorithm is presented for solving this split common problem. …”
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Neural Network to Solve Concave Games by Zixin Liu, Nengfa Wang

“…Combined with variational inequality, Ky Fan inequality, and projection equation, concave games are transformed into a neural network model. …”
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Common Fixed-Point Problem for a Family Multivalued Mapping in Banach Space by Zhanfei Zuo

“…Moreover, it is the unique solution in 𝐹 to a certain variational inequality, where 𝐹∶=∩∞𝑛=0𝐹(𝑇𝑛) stands for the common fixed-point set of the family of multivalued nonexpansive mapping {𝑇𝑛}.…”
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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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