On the rate of convergence of the Szász-Mirakyan operator for functions of bounded variation (Q788934)

In this paper the rate of convergence of the Szász-Mirakyan operator \(S_ n(f,x)\) for functions of bounded variation on every finite subinterval of \([0,\infty)\) is studied. The author proves that \(S_ n(f,x)\) converges to \(frac{1}{2}(f(x+)+(f(x-))\) under Hermann's condition on the magnitude of f by giving quantitative estimates of the rate of convergence. These estimates are essentially best possible.