Convergence of linking Baskakov-type operators (Q2003787)

The authors investigate the convergence properties of linking Baskakov-Durrmeyer type operators \(B_{n,\rho}^{[c]}\) for \(c>0\) when the linking parameter \(\rho\) tends to infinity. The purpose of this paper is to prove the uniform convergence of \(B_{n,\rho}^{[c]}f\) to \(B_{n,\infty}^{[c]}f\) on every interval \([0,b]\) when \(\rho \to \infty,\) where \(f\) is an arbitrary continuous function on \([0,\infty)\) satisfying a polynomial growth condition, and \(B_{n,\infty}^{[c]}\) is the usual Baskakov type operator.