Direct estimates in simultaneous approximation for BBS operators

The summation integral type Baskakov-Beta operator were introduced by Gupta [V. Gupta, A note on modified Baskakov type operators, Approx. Theory Appl. 10 (3) (1994) 74-78]. In the present paper, we extend our studies and introduce the Baskakov-Beta-Stancu (abbr. BBS) operator, we give the moments of these operators using hypergeometric series, in the next section we derive the asymptotic formula and error estimation in simultaneous approximation. In the end we propose an open problem to the readers.