Extremal Approximately Convex Functions and Estimating the Size of Convex Hulls

S. J. Dilworth, Ralph Howard, James W. Roberts

A real valued function $f$ defined on a convex $K$ is anemconvex function iff it satisfies $$f((x+y)/2)\le (f(x)+f(y))/2+1.$$ A thorough study of approximately convex function…