From Fixed Point Regularization to Constraint Decomposition in Variational Inequalities

We consider a triple hierarchical variational inequality problem (THVIP), that is, a variational inequality problem defined over the set of solutions of another variational inequality problem which is defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Moreover, we propose a multistep hybrid extragradient method to compute the approximate solutions of the THVIP and present the convergence analysis of the sequence generated by the proposed method. We also derive a solution method for solving a system of hierarchical variational inequalities (SHVI), that is, a system of variational inequalities defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Under very mild conditions, it is proven that the sequence generated by the proposed method converges strongly to a unique solution of the SHVI.

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A generalized cyclic iterative method for solving variational inequalities over the solution set of a split common fixed point problem

Numerical Algorithms ◽

10.1007/s11075-021-01252-0 ◽

2022 ◽

Author(s):

Simeon Reich ◽

Truong Minh Tuyen

Keyword(s):

Fixed Point ◽

Iterative Method ◽

Variational Inequalities ◽

Common Fixed Point ◽

Fixed Point Problem ◽

Solution Set ◽

Point Problem ◽

Common Fixed Point Problem ◽

Split Common Fixed Point

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RELAXED EXTRAGRADIENT METHOD FOR FINDING A COMMON ELEMENT OF SYSTEMS OF VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS

Taiwanese Journal of Mathematics ◽

10.11650/tjm.17.2013.2198 ◽

2013 ◽

Vol 17 (2) ◽

pp. 701-724 ◽

Cited By ~ 2

Author(s):

L.-C. Ceng ◽

M.-M Wong

Keyword(s):

Fixed Point ◽

Variational Inequalities ◽

Extragradient Method ◽

Fixed Point Problems ◽

Common Element ◽

Systems Of Variational Inequalities

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STRONG CONVERGENCE OF AN ITERATIVE ALGORITHM FOR SYSTEMS OF VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS IN q-UNIFORMLY SMOOTH BANACH SPACES

Korean Journal of Mathematics ◽

10.11568/kjm.2012.20.2.225 ◽

2012 ◽

Vol 20 (2) ◽

pp. 225-237

Author(s):

Jae Ug Jeong

Keyword(s):

Fixed Point ◽

Variational Inequalities ◽

Strong Convergence ◽

Banach Spaces ◽

Iterative Algorithm ◽

Fixed Point Problems ◽

Uniformly Smooth ◽

Systems Of Variational Inequalities ◽

Uniformly Smooth Banach Spaces

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Viscosity explicit midpoint methods for nonexpansive mappings in Hadamard spaces

Filomat ◽

10.2298/fil2004347p ◽

2020 ◽

Vol 34 (4) ◽

pp. 1347-1357

Author(s):

Pakkapon Preechasilp

Keyword(s):

Fixed Point ◽

Variational Inequalities ◽

Equilibrium Problem ◽

Nonexpansive Mappings ◽

Midpoint Method ◽

Approximating Sequence

In this paper, the viscosity explicit midpoint method for nonexpansive mappings in Hadamard spaces is introduced. Under certain appropriate conditions on the sequence of parameters, it is proved that the limit of the approximating sequence generated by proposed method converges strongly to a fixed point of T which solves some variational inequalities. Moreover, we give an application to the equilibrium problem.

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A New Viscosity Cesàro Mean Approximation Method for a General System of Finite Variational Inequalities and Fixed Point Problems in Banach Spaces

Lecture Notes in Electrical Engineering - Transactions on Engineering Technologies ◽

10.1007/978-94-007-7684-5_29 ◽

2013 ◽

pp. 419-434

Author(s):

Poom Kumam ◽

Somyot Plubtieng ◽

Phayap Katchang

Keyword(s):

Fixed Point ◽

Variational Inequalities ◽

Banach Spaces ◽

Approximation Method ◽

General System ◽

Fixed Point Problems ◽

Cesàro Mean ◽

Cesaro Mean

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An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems

Mathematics ◽

10.3390/math7010061 ◽

2019 ◽

Vol 7 (1) ◽

pp. 61 ◽

Cited By ~ 18

Author(s):

Yonghong Yao ◽

Mihai Postolache ◽

Jen-Chih Yao

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Variational Inequalities ◽

Strong Convergence ◽

Fixed Points ◽

Iterative Algorithm ◽

Nonlinear Transformation ◽

Generalized Variational Inequalities ◽

Generalized Variational Inequality ◽

Suggested Algorithm

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested algorithm is demonstrated.

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Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities, and Fixed Point Problems

Mathematics ◽

10.3390/math7020187 ◽

2019 ◽

Vol 7 (2) ◽

pp. 187

Author(s):

Lu-Chuan Ceng ◽

Qing Yuan

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Variational Inequalities ◽

General System ◽

Inequality Constraint ◽

Fixed Point Problem ◽

Point Problem ◽

Common Solution ◽

Common Fixed Point Problem ◽

Monotone Variational Inequality

In this paper, we introduce a multiple hybrid implicit iteration method for finding a solution for a monotone variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities, and a common fixed point problem of a countable family of uniformly Lipschitzian pseudocontractive mappings and an asymptotically nonexpansive mapping in Hilbert spaces. Strong convergence of the proposed method to the unique solution of the problem is established under some suitable assumptions.

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