On the Order of Approximation of Unbounded Functions by Positive Linear Operators

Recently there has been a great amount of research both qualitative and quantitative on the problem of approximating functions with certain growth conditions by means of linear positive operators. This paper discusses a quantitative problem for unbounded functions, i.e., the order of approximation to unbounded functions by means of linear positive operators.The theorems presented are, in several instances, extensions of known results from the case of bounded functions to the unbounded case. Applications of these theorems are given to spline functions, which are presently the subject of intensive investigation, and to the well-known Szasz-Mirakyan-Hille operators.