Remarks about Scalar Equilibrium Problems

Abstract: We make an introduction showing the importance of the Scalar Equilibrium Problem which consists of: find a point x in some set K such that a function f(x,y) is greater or equal to zero for all y in K, where K is a nonempty closed convex subset in a real reflexive Banach space, f(x,x) = 0 for each x in K, f is convex and lower semicontinuous in the second argument and upper semi-continuous in the first one. After that we talk about our recents contributions concerning existence results and duality theory.