Approximation error for linear polynomial interpolation on n-simplices

Let W(n)(2)M be the class of functions f: Delta(n) --> R (when Delta(n) is an n-simplex) with bounded second derivative (whose absolute value does not exceed M > 0) along any direction at an arbitrary point;of the simplex Delta(n). Let P-l,P-n(f; x) be the linear polynomial interpolating f at the vertices of the simplex. We prove that there exists a function g is an element of W(n)(2)M such that for any f is an element of W(n)(2)M and any x is an element of Delta(n), one has \f(x) - P-l,P-n(f; x)\ less than or equal to g(x).