Content:
It shown that a number of equilibrium problems and related variational inequalities can be cast as finding the maxinf (or minsup) or saddle points of bivariate functions. We can then appeal to the theory of lopsided convergence for bivariate functions to derive stability results. In this introductory paper, we limit ourself to situations when the bivariate function is generated by single-valued mappings. A subsequent paper will deal with situations when this mapping can also be set-valued.
March 2005