Abstract
In this work, we first define the generalized 2 − g KKM mapping and the family 2 − g KKM ( X , Y ) in a hyperconvex metric space, and we get a fixed point theorem on this family without compact assumption. Next, we establish some variational inequalities and minimax inequalities for the family 2 − g KKM ( X , Y ) and the Φ -mapping.
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