scholarly journals Auxiliary principle technique for solving regularized nonconvex mixed equilibrium problems

2019 ◽  
Vol 20 (2) ◽  
pp. 431-450
Author(s):  
Qamrul Hasan Ansari ◽  
◽  
Javad Balooee ◽  
Keyword(s):  
Equilibrium Problems ◽  
Auxiliary Principle ◽  
Auxiliary Principle Technique ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

scholarly journals On a System of Generalized Mixed Equilibrium Problems Involving Variational-Like Inequalities in Banach Spaces: Existence and Algorithmic Aspects

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
H. Mahdioui ◽  
O. Chadli
Keyword(s):  
Banach Spaces ◽  
Equilibrium Problems ◽  
Auxiliary Problem ◽  
Auxiliary Principle ◽  
Auxiliary Principle Technique ◽  
Generalized Mixed Equilibrium Problems ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Algorithmic Aspect ◽  
Mixed Equilibrium

We study the existence and the algorithmic aspect of a System of Generalized Mixed Equilibrium Problems involving variational-like inequalities (SGMEPs) in the setting of Banach spaces. The approach adopted is based on the auxiliary principle technique and arguments from generalized convexity. A new existence theorem for the auxiliary problem is established; this leads us to generate an algorithm which converges strongly to a solution of (SGMEP) under weaker assumptions. When the study is reduced to the setting of reflexive Banach spaces, then it can be more relaxed by dropping the coercivity condition. The results obtained in this paper are new and improve some recent studies in this field.

scholarly journals An inertial based forward–backward algorithm for monotone inclusion problems and split mixed equilibrium problems in Hilbert spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yasir Arfat ◽  
Poom Kumam ◽  
Parinya Sa Ngiamsunthorn ◽  
Muhammad Aqeel Ahmad Khan
Keyword(s):  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Monotone Inclusion ◽  
Inclusion Problems ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

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.

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