Summary: We apply a new fixed-point theorem [L.-J. Lin
and Z.-T. Yu
, Nonlinear Anal., Theory Methods Appl. 43A, 987-999 (2001; Zbl 0989.47051
)] and use various monotonicity and some coercivity conditions to establish equilibrium theorems for multimaps in generalized convex spaces of S. Park
and H. Kim
[J. Math. Anal. Appl. 197, 173-187 (1996; Zbl 0851.54039
)]. As a simple consequence, we give a unified approach to vectorial equilibria for multimaps. We show that, from our results, some well-known classical results, such as the Ky Fan minimax inequality theorem and the Browder and Hartman-Stampacchia theorems concerning the existence for variational inequalities, can be derived easily.