Before revision: We describe and examine a test for  shape constraints, such as monotonicity, convexity (or both simultaneously) , U-shape, S-shape and others, in a nonparametric framework using partial sums empirical processes.
After revision: We describe and examine a test for a general class of shape constraints, such as monotonicity, convexity (or both simultaneously) , U-shape, S-shape and others, in a nonparametric framework using partial sums empirical processes.