scholarly journals Strong Duality and Optimality Conditions for Generalized Equilibrium Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
D. H. Fang ◽  
J. F. Bao
Keyword(s):  
Optimality Conditions ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Necessary Conditions ◽  
Strong Duality ◽  
Conjugate Functions ◽  
Generalized Equilibrium Problem ◽  
Dc Functions ◽  
Duality Results ◽  
Generalized Equilibrium

We consider a generalized equilibrium problem involving DC functions. By using the properties of the epigraph of the conjugate functions, some sufficient and/or necessary conditions for the weak and strong duality results and optimality conditions for generalized equilibrium problems are provided.

scholarly journals Generalized Equilibrium Problems Related to Ky Fan Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ionel Rovenţa
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Generalized Equilibrium Problem ◽  
Type Algorithm ◽  
Generalized Equilibrium ◽  
Ky Fan Inequalities ◽  
Ky Fan ◽  
Point Type

We study a generalized equilibrium problem by using a nonsymmetric extension of Ky Fan’s inequality. As an application, we present a fixed point type algorithm inspired by a model from Tada and Takahashi (2007).

scholarly journals Viscosity Approximations by the Shrinking Projection Method of Quasi-Nonexpansive Mappings for Generalized Equilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-30 ◽  
Author(s):  
Rabian Wangkeeree ◽  
Nimit Nimana
Keyword(s):  
Fixed Points ◽  
Equilibrium Problem ◽  
Projection Method ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Generalized Equilibrium Problem ◽  
Shrinking Projection Method ◽  
Generalized Equilibrium

We introduce viscosity approximations by using the shrinking projection method established by Takahashi, Takeuchi, and Kubota, for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of a quasi-nonexpansive mapping. Furthermore, we also consider the viscosity shrinking projection method for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of the super hybrid mappings in Hilbert spaces.

scholarly journals Iterative Computation for Solving the Variational Inequality and the Generalized Equilibrium Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Xiujuan Pan ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Convergence Result ◽  
Generalized Equilibrium Problem ◽  
Iterative Computation ◽  
Generalized Equilibrium

An iterative algorithm for solving the variational inequality and the generalized equilibrium problem has been introduced. Convergence result is given.

Duality for generalized equilibrium problem

Optimization ◽  
2008 ◽  
Vol 57 (6) ◽  
pp. 795-805 ◽  
Author(s):  
Flávia Morgana O. Jacinto ◽  
Susana Scheimberg**
Keyword(s):  
Equilibrium Problem ◽  
Generalized Equilibrium Problem ◽  
Generalized Equilibrium
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