On a Class of Bernstein-Type Rational Functions

摘要

This note aims to highlight a general class of discrete linear and positive operators, focusing on some of their approximation properties. The construction includes a sequence of positive numbers strictly decreasing. Imposing additional conditions on it, we set the convergence of the operators towards the identity operator and establish upper bounds for the error of approximation. A probabilistic approach is given. Also, in certain weighted spaces the study of its approximation properties is developed.