Relations Between the Bernstein Polynomials and q-monotone Functions
Relations Between the Bernstein Polynomials and q-monotone Functions
Abstract We show that certain inequalities involving differences of the Bernstein basis polynomials and values of a function $$f\in C[0,1]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>C</mml:mi> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> , imply that the function is q -monotone. In view of previous results of the authors (see …