Simultaneous approximation by Baskakov-Durrmeyer operator (Q2744457)

For functions \(f\) defined on the interval \([0,\infty)\), the Baskakov-Durrmeyer operator is given by NEWLINE\[NEWLINE\widetilde V_n(f, x)= \sum^\infty_{k=0} (n-1) v_{n,k}(x) \int^\infty_0 f(t)v_{n,k})t) dt,NEWLINE\]NEWLINE where \(v_{n,k}(x)= \left(\begin{smallmatrix} n+k-1\\ k\end{smallmatrix}\right) x^k(1+ x)^{-n-k}\). The authors investigate the degree of simultaneous approximation by means of these operators for functions whose derivatives have only discontinuity points of the first kind on \([0,\infty)\) and which are of exponential growth and prove quantitative statements involving the first-order modulus of continuity.