Rate of convergence for the modified Szász-Mirakyan operators on functions of bounded variation
The modified Szász-Mirakyan operators are defined by \[ M_n(f,x)= n\sum^\infty_{k= 0} p_k(nx) \int^\infty_0 p_k(nt) f(t) dt, \] where \(p_k(s)= e^{-s} s^k/k!\). The authors obtain an estimate of the rate of convergence on functions of bounded variation. Their results improve and correct some estimates of \textit{A. Sahai} and \textit{G. Prasad} [Publ. Inst. Math., Nouv. Sér. 53, 73-80 (1993; Zbl 0795.41019)] and \textit{V. Gupta} and \textit{P. N. Agrawal} [ibid. 49(63), 97-103 (1991; Zbl 0738.41025)].
scientific article; zbMATH DE number 1295257