Abstract
In this paper, we introduce the concept of the strict Kakutani multimap (KKM) property and investigate the fixed point problem for multimaps having this property on almost Γ -convex subsets of locally G -convex uniform spaces. Our new fixed point theorem generalizes the well-known Fan–Glicksberg fixed point theorem and partially extends the Himmelberg fixed point theorem. Its application to minimax theorem is also given.
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