Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove this sort is inherited by the convex envelope, which key to obtain other remarkable properties such as coercivity. Our techniques allow retrieve Enflo's uniformly renorming super-reflexive Banach spaces regularization raw function built from trees. Among appl...

(1) /(*i)+ƒ(**) = / ( * i + * 2 ) for all real Xi and x^ I think you would enjoy reading Cauchy's elegant treatment of this simple problem. But possibly you would enjoy more solving it yourself, or seeing to what considerations you are led if you omit the hypothesis of continuity. The discontinuous solutions of (1) have been studied extensively. I have mentioned this equation because any soluti...