Saturation and Inverse Theorems for Combinations of a Class of Exponential-Type Operators

Abstract

Rates of convergence, saturation theorems and the socalled “inverse problems” for Bernstein polynomials have been intensively studied (see, e.g., [1 ; 4; 8; 14; 17]). The same problems for some other positive operators have also been investigated by many authors. In this paper, we shall use a uniform approach to study the saturation and inverse problems for a class of linear combinations of operators including Bernstein polynomials, and Szâsz, Post-Widder, Gauss-Weierstrass and Baskakov operators.