A note on reflexivity and nonconvexity Original Research Article

In this short note we prove that a Banach space XX is reflexive if, and only if, the Eisenfeld–Lakshmikantham measure of nonconvexity in XX satisfies the Cantor property. Using this characterization, some results in best approximation and fixed point theory for reflexive Banach spaces are generalized by removing convexity requirements.