Abstract :
The concept of concavity is generalized to discrete functions, u, satisfying the nth-order difference inequality, (−1)n−kΔnu(m) ≥ 0, m= 0, 1,..., N and the homogeneous boundary conditions, u(0) = … = u(k−1) = 0, u(N + k + 1) = … = u(N + n) = 0 for some k “1, ..., n − 1”. A piecewise polynomial is constructed which bounds u below. The piecewise polynomial is employed to obtain a positive lower bound on u(m) for m = k, ..., N + k, where the lower bound is proportional to the supremum of u. An analogous bound is obtained for a related Greenʹs function.
