Squared basis operators related to Bessel functions

Abstract

Recent studies on linear positive operators have led to the investigation of approximation properties of Szász–Mirkyan operators related to the modified Bessel function of order 0. In this paper, we analyse the asymptotic behavior of these operators, convergence theorems, Voronovskaya and Grüss-Voronovskaya type results. A comparative assessment with classical Szász–Mirakyan operators is also presented. These results may have an impact on wide branches of knowledge, such as probability theory, statistics, physical chemistry, optics, and computer science, especially signal processing.