The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems

We introduce a modified Mann’s iterative procedure by using the hybrid projection method for solving the common solution of the system of equilibrium problems for a finite family of bifunctions satisfying certain condition, the common solution of fixed point problems for two finite families of quasi-ϕ-nonexpansive mappings, and the common solution of variational inequality problems for a finite family of continuous monotone mappings in a uniformly smooth and strictly convex real Banach space. Then, we prove a strong convergence theorem of the iterative procedure generated by some mild conditions. Our result presented in this paper improves and generalizes some well-known results in the literature.

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An iterative algorithm for the system of split mixed equilibrium problem

Demonstratio Mathematica ◽

10.1515/dema-2020-0027 ◽

2020 ◽

Vol 53 (1) ◽

pp. 309-324

Author(s):

Ibrahim Karahan ◽

Lateef Olakunle Jolaoso

Keyword(s):

Variational Inequality ◽

Iterative Algorithm ◽

Equilibrium Problems ◽

Nonexpansive Mappings ◽

Equilibrium System ◽

Convergence Conditions ◽

Mixed Equilibrium Problems ◽

Split Variational Inequality ◽

Mixed Equilibrium ◽

Split Mixed Equilibrium Problem

AbstractIn this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.

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Modified block iterative method for solving convex feasibility problem, equilibrium problems and variational inequality problems

Acta Mathematica Sinica English Series ◽

10.1007/s10114-011-0099-3 ◽

2011 ◽

Vol 28 (4) ◽

pp. 741-758 ◽

Cited By ~ 3

Author(s):

Shi Sheng Zhang ◽

Chi Kin Chan ◽

H. W. Joseph Lee

Keyword(s):

Variational Inequality ◽

Iterative Method ◽

Equilibrium Problems ◽

Convex Feasibility Problem ◽

Variational Inequality Problems ◽

Feasibility Problem ◽

Convex Feasibility ◽

Modified Block

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PARALLEL EXTRAGRADIENT-PROXIMAL METHODS FOR SPLIT EQUILIBRIUM PROBLEMS

Mathematical Modelling and Analysis ◽

10.3846/13926292.2016.1183527 ◽

2016 ◽

Vol 21 (4) ◽

pp. 478-501 ◽

Cited By ~ 35

Author(s):

Dang Van Hieu

Keyword(s):

Variational Inequality ◽

Strong Convergence ◽

Projection Method ◽

Equilibrium Problems ◽

Extragradient Method ◽

Variational Inequality Problems ◽

Proximal Methods ◽

Proximal Method ◽

Weak And Strong Convergence ◽

Split Variational Inequality

In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. We also present an application to split variational inequality problems and a numerical example to illustrate the convergence of the proposed algorithms.

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