A modified projection method for a common solution of a system of variational inequalities, a split equilibrium problem and a hierarchical fixed-point problem

AbstractIn this paper, we suggest and analyze an iterative algorithm to approximate a common solution of a hierarchical fixed point problem for nonexpansive mappings, a system of variational inequalities, and a split equilibrium problem in Hilbert spaces. Under some suitable conditions imposed on the sequences of parameters, we prove that the sequence generated by the proposed iterative method converges strongly to a common element of the solution set of these three kinds of problems. The results obtained here extend and improve the corresponding results of the relevant literature.

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Strong convergence for monotone bilevel equilibria with constraints of variational inequalities and fixed points using subgradient extragradient implicit rule

Journal of Inequalities and Applications ◽

10.1186/s13660-021-02683-y ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Long He ◽

Yun-Ling Cui ◽

Lu-Chuan Ceng ◽

Tu-Yan Zhao ◽

Dan-Qiong Wang ◽

...

Keyword(s):

Fixed Point ◽

Variational Inequalities ◽

Strong Convergence ◽

Equilibrium Problem ◽

Real Hilbert Space ◽

Nonexpansive Mappings ◽

Fixed Point Problem ◽

Point Problem ◽

Common Solution ◽

Implicit Rule

AbstractIn a real Hilbert space, let GSVI and CFPP represent a general system of variational inequalities and a common fixed point problem of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping, respectively. In this paper, via a new subgradient extragradient implicit rule, we introduce and analyze two iterative algorithms for solving the monotone bilevel equilibrium problem (MBEP) with the GSVI and CFPP constraints, i.e., a strongly monotone equilibrium problem over the common solution set of another monotone equilibrium problem, the GSVI and the CFPP. Some strong convergence results for the proposed algorithms are established under the mild assumptions, and they are also applied for finding a common solution of the GSVI, VIP, and FPP, where the VIP and FPP stand for a variational inequality problem and a fixed point problem, respectively.

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Implicit iterative method for approximating a common solution of split equilibrium problem and fixed point problem for a nonexpansive semigroup

Arab Journal of Mathematical Sciences ◽

10.1016/j.ajmsc.2013.04.002 ◽

2014 ◽

Vol 20 (1) ◽

pp. 57-75 ◽

Cited By ~ 4

Author(s):

K.R. Kazmi ◽

S.H. Rizvi

Keyword(s):

Fixed Point ◽

Iterative Method ◽

Equilibrium Problem ◽

Fixed Point Problem ◽

Nonexpansive Semigroup ◽

Point Problem ◽

Split Equilibrium Problem ◽

Common Solution ◽

Implicit Iterative Method

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Iterative approximation of a common solution of a split equilibrium problem, a variational inequality problem and a fixed point problem

Journal of the Egyptian Mathematical Society ◽

10.1016/j.joems.2012.10.009 ◽

2013 ◽

Vol 21 (1) ◽

pp. 44-51 ◽

Cited By ~ 32

Author(s):

K.R. Kazmi ◽

S.H. Rizvi

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Equilibrium Problem ◽

Variational Inequality Problem ◽

Fixed Point Problem ◽

Point Problem ◽

Iterative Approximation ◽

Split Equilibrium Problem ◽

Inequality Problem ◽

Common Solution

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Algorithms of common solutions for a variational inequality, a split equilibrium problem and a hierarchical fixed point problem

Fixed Point Theory and Applications ◽

10.1186/1687-1812-2013-278 ◽

2013 ◽

Vol 2013 (1) ◽

Cited By ~ 4

Author(s):

Abdellah Bnouhachem

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Equilibrium Problem ◽

Fixed Point Problem ◽

Point Problem ◽

Split Equilibrium Problem ◽

Hierarchical Fixed Point Problem ◽

Hierarchical Fixed Point

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A New Hybrid Extragradient Iterative Method for Approximating the Common Solutions of a System of Variational Inequalities, a Mixed Equilibrium Problem, and a Hierarchical Fixed Point Problem

Abstract and Applied Analysis ◽

10.1155/2013/737590 ◽

2013 ◽

Vol 2013 ◽

pp. 1-19

Author(s):

Abdellah Bnouhachem ◽

Abdelouahed Hamdi

Keyword(s):

Fixed Point ◽

Variational Inequalities ◽

Equilibrium Problem ◽

Fixed Point Problem ◽

Point Problem ◽

Mixed Equilibrium Problem ◽

System Of Variational Inequalities ◽

Hierarchical Fixed Point Problem ◽

Hierarchical Fixed Point ◽

The Common

We suggest and analyze an iterative scheme for finding the approximate element of the common set of solutions of a system of variational inequalities, a mixed equilibrium problem, and a hierarchical fixed point problem in a real Hilbert space. Strong convergence of the proposed method is proved under some conditions. The results presented in this paper extend and improve some well-known results in the literature.

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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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