A generalized KKMF principle

Abstract: We present in this paper a generalized version of the celebrated Knaster–Kuratowski–Mazurkiewicz–Fan''s principle on the intersection of a family of closed sets subject to a classical geometric condition and a weakened compactness condition. The fixed point formulation of this generalized principle extends the Browder–Fan fixed point theorem to set-valued maps of non-compact convex subsets of topological vector spaces. [Copyright &y& Elsevier]