In this paper we present direct approximation results for Mellin-Fejer type operators. In particular we are interested in quantitative approximation theorems in Mellin-Lebesgue spaces, using a suitable modulus of smoothness. Furthermore, an asymptotic formula of Voronovskaya type is obtained. Introducing a new modulus of smoothness, called logarithmic weighted modulus of smoothness in the weighted Mellin-Lebesgue spaces, a rate of convergence is obtained and the global smoothness preservation property is also expressed through the new modulus of smoothness. The present results represent a completion of the theory developed in recent years on this subject. Finally, we illustrate some particular examples of kernel functions satisfying the assumptions of the theorems.
A note on the Mellin-Fejer Kernels
Carlo Bardaro;Ilaria Mantellini;
2025
Abstract
In this paper we present direct approximation results for Mellin-Fejer type operators. In particular we are interested in quantitative approximation theorems in Mellin-Lebesgue spaces, using a suitable modulus of smoothness. Furthermore, an asymptotic formula of Voronovskaya type is obtained. Introducing a new modulus of smoothness, called logarithmic weighted modulus of smoothness in the weighted Mellin-Lebesgue spaces, a rate of convergence is obtained and the global smoothness preservation property is also expressed through the new modulus of smoothness. The present results represent a completion of the theory developed in recent years on this subject. Finally, we illustrate some particular examples of kernel functions satisfying the assumptions of the theorems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
