Abstract: According to the property of demi(sub)martingales, using the property of convex function and the indicative function, we gave a class of minimal inequalities for demi(sub)martingales under the condition that the product of the left derivative h(x) of the convex function g(x) and some of the indicative functions was a nonnegative function with respect to nondecreasing components.

Key words: demimartingale, demisubmartingale, minimal inequality