Abstract
AbstractGiven a nonempty convex subset X of a topological vector space and a real bifunction f defined on $$X \times X$$
X
×
X
, the associated equilibrium problem consists in finding a point $$x_0 \in X$$
x
0
∈
X
such that $$f(x_0, y) \ge 0$$
f
(
x
0
,
y
)
≥
0
, for all $$y \in X$$
y
∈
X
. A standard condition in equilibrium problems is that the values of f to be nonnegative on the diagonal of $$X \times X$$
X
×
X
. In this paper, we deal with equilibrium problems in which this condition is missing. For this purpose, we will need to consider, besides the function f, another one $$g: X \times X \rightarrow \mathbb {R}$$
g
:
X
×
X
→
R
, the two bifunctions being linked by a certain compatibility condition. Applications to variational inequality problems, quasiequilibrium problems and vector equilibrium problems are given.
Publisher
Springer Science and Business Media LLC
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