New existence results for equilibrium problems

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A subgradient-type method for the equilibrium problem over the fixed point set and its applications (2009, background): “Equilibrium problem The equilibrium problem [3–6,11,15,16,20,23,24] has been studied widely in the context of optimization problems, fixed point problems, variational inequality problems, complementarity problems, Nash equilibrium problems and so on.”
On the proximal point method for equilibrium problems in Hilbert spaces (2010, background): “We prove instead that under mild monotonicity-like assumptions on f, the problem EPð ~ f,K Þ always has solutions, as a consequence of the existence result for equilibrium problems introduced in [9,6].”
An inexact subgradient algorithm for Equilibrium Problems (2011, background): “Furthermore, this example gives a negative answer to the conjecture given in [9], namely, if C is a nonempty, convex and closed set such that f (x, x) = 0, f (x, ∙) : C → R is convex and lower semi-continuous, f (∙, y) : C → R is upper semi-continuous for all x ∈ C and the primal and dual equilibriu”
On the Maximal Monotonicity of Diagonal Subdifferential Operators (2010, background): “Several variants of this condition were originally introduced in [7] and further analyzed in [6].”