Monotonicity conditions for a sequence of generalized polynomials of S. N. Bernshtein and A. O. Gel'fond

It is shown that the sequence of generalized polynomials of S. N. Bernshtein and A. O. Gel'fond, which corresponds to a function $f(x)$, is an increasing or decreasing sequence depending on the concavity or convexity of the function. Analogous results are given in the case of functions of two variables.