A Generalized Variational Principle and Its Application to Equilibrium Problems

In this paper, we prove a generalized Ekeland-type variational principle for bifunctions, by showing the existence of solution for some generalized optimization problems. In a particular case, from this result, we obtain a Zhong-type variational principle for bifunctions, which may be important from algorithmic point of view, because the solution can be localized in a sphere. Contrary to the standard literature, we are able to guarantee the existence of solution without assuming the triangle property.