scholarly journals Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings

2016 ◽  
Vol 73 (1) ◽  
pp. 197-217 ◽  
Author(s):  
Dang Van Hieu ◽  
Le Dung Muu ◽  
Pham Ky Anh
Keyword(s):  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Extragradient Methods ◽  
Parallel Hybrid ◽  
Hybrid Extragradient Methods

Two new extragradient methods for solving equilibrium problems

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
Habib ur Rehman ◽  
Aviv Gibali ◽  
Poom Kumam ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Equilibrium Problems ◽  
Extragradient Methods

Modified proximal-like extragradient methods for two classes of equilibrium problems in Hilbert spaces with applications

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Habib ur Rehman ◽  
Poom Kumam ◽  
Ioannis K. Argyros ◽  
Nasser Aedh Alreshidi
Keyword(s):  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Extragradient Methods

scholarly journals An iterative algorithm for the system of split mixed equilibrium problem

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.

scholarly journals Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Tanom Chamnarnpan ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Monotone Mapping ◽  
Iterative Algorithms ◽  
Infinite Family ◽  
Common Element ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for aβ-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part.

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