On a q-analog of the Baskakov basis functions

Recently, Agrawal and Thamer suggested a new sequence of summation-integral type operators using the Baskakov basis function. We find a generating function of the q -Baskakov basis function and suggest a q -analog of the operators. We estimate moments, give a recurrence formula, and obtain some direct results. We also mention the possibility of improving the q -operators and, finally, suggest a Bézier-type variant of the operators discussed here.