On well-posedness of generalized equilibrium problems involving -monotone bifunction

Abstract

The aim of this paper is to establish some uniqueness and well-posedness results for a general inequality of equilibrium problems type involving -monotone bifunction, whose solution is sought in a subset K of a Banach space X. Some metric character- izations and sucient conditions for these types of well-posedness are obtained. Moreover, we prove that the well-posedness of gen- eralized equilibrium problems is equivalent to the existence and uniqueness of its solution.

Keywords

• equilibrium problems
• well-posed optimization problems
• monotonicity
• metric characterizations