Monotonicity, Convexity and Symmetric Derivates

Abstract

If the first lower symmetric derivate of a continuous function is nonnegative, then it is nondecreasing. If the second lower symmetric derivate of a continuous function is nonnegative, then it is convex. In this paper it is shown that if continuity is replaced by Baire one, Darboux in each of these, then the resulting statements are true.