Gupta, Vijay; Srivastava, G. S.; Sahai, A. On simultaneous approximation by Szász-beta operators. (English) Zbl 0846.41022 Soochow J. Math. 21, No. 1, 1-11 (1995). The authors have defined a new sequence of linear positive operators by coupling Szász and beta operators as \[ B_n (f; x)= \sum^\infty_{k=0} p_{n,k} (x) \int^\infty_0 b_{n,k} (y) f(y) dy, \qquad x\in [0, \infty) \] where \[ p_{n,k} (x)= e^{-nx} {{(nx)^k} \over {k!}} \quad \text{ and } \quad b_{n,k} (y)= {1\over {\beta(k+ 1,n)}} {y^k \over {(1+ y)^{n+k +1}}}. \] The main result of the paper is the Woronowskaja type asymptotic formula in simultaneous approximation for Lebesgue integrable functions. The next result is the local estimate for the \(r\)th derivative of the function. Finally, the claim that the main theorem has improved the earlier results on modified Baskakov and Szász operators by H. S. Kasana, P. N. Agrawal and V. Gupta [Approximation Theory Appl. 7, No. 2, 65-82 (1991; Zbl 0755.41024)]. Reviewer: H.S.Kasana (Pilani) Cited in 1 ReviewCited in 14 Documents MSC: 41A36 Approximation by positive operators Keywords:Taylor expansion; beta operators; asymptotic formula; simultaneous approximation; Szász operators Citations:Zbl 0755.41024 PDFBibTeX XMLCite \textit{V. Gupta} et al., Soochow J. Math. 21, No. 1, 1--11 (1995; Zbl 0846.41022)