Using techniques of convex analysis, we provide a direct proof of a recent characterization of convexity given in the setting of Banach spaces in [J. Saint Raymond, J. Nonlinear Convex Anal., 14 (2013), pp. 253--262]. Our results also extend this characterization to locally convex spaces under weaker conditions.
['Rafael Correa', 'Abderrahim Hantoute', 'Pedro Pérez-Aros']
On the Klee--Saint Raymond's Characterization of Convexity