Quantitative Voronovskaya-Type Theorems for Fejér-Korovkin Operators

Abstract

In recent times, quantitative Voronovskaya type theorems have been presented in spaces of non-periodiccontinuous functions. In this work, we proved similar results but for Fejér-Korovkin trigonometric operators. That iswe measure the rate of convergence in the associated Voronovskaya type theorem. Recall that these operators providethe optimal rate in approximation by positive linear operators. For the proofs, we present new inequalities relatedwith trigonometric polynomials as well as with the convergence factor of the Fejér-Korovkin operators. Our approachincludes spaces of Lebesgue integrable functions.