Abstract In this paper, we study the existence of solutions for equilibrium problems in which the bifunction involved is defined on the Cartesian product of two distinct sets. Such a problem will be called a generalized equilibrium problem. The proofs we propose for establishing the existence theorems do not rely on classical tools, such as KKM-type theorems or separation theorems. Instead, as we will see, they are based on an intersection theorem established by Bassanezi and Greco 11. Upper semicontinuity in the first variable of a given bifunction is a standard condition when seeking solutions to a classical equilibrium problem. In this paper, we introduce a concept that refines upper semicontinuity, called marginal r -upper semicontinuity. In our existence results, it will suffice as the bifunction to be marginally 0-upper semicontinuous in the first variable.
Mircea Balaj (Wed,) studied this question.