On the Approximation by Balázs–Szabados Operators

Abstract

We present three new approximation properties of the Balázs–Szabados operators. Firstly, we prove that, in certain cases, these operators approximate some super-exponential functions on compact intervals. Next, we provide a new estimate of the error of approximation using a suitable modulus of continuity. Finally, we characterize the functions which can be uniformly approximated in the weighted norm of polynomial weight spaces.

Keywords

• positive linear operators
• Balázs operators
• rational Bernstein type operators
• weighted spaces
• modulus of continuity
• tail inequality