Relations Between the Bernstein Polynomials and q-monotone Functions.

We show that certain inequalities involving differences of the Bernstein basis polynomials and values of a function f ∈ C [ 0 , 1 ] , imply that the function is q-monotone. In view of previous results of the authors (see the list of references), the current results provide, among others, a characterization of q-monotone functions in C[0, 1]. [ABSTRACT FROM AUTHOR]