Quantitative estimates for Durrmeyer-sampling series in Orlicz spaces

Abstract

AbstractIn this paper, we establish a quantitative estimate for Durrmeyer-sampling type operators in the general framework of Orlicz spaces, using a suitable modulus of smoothness defined by the involved modular functional. As a consequence of the above result, we can deduce quantitative estimates in several instances of Orlicz spaces, such as $$L^p$$ L p -spaces, Zygmund spaces and the exponential spaces. By using a direct approach, we also provide a further estimate in the particular case of $$L^p$$ L p -spaces, with $$1\le p <+\infty $$ 1 ≤ p < + ∞ , that turns out to be sharper than the previous general one. Moreover, we deduce the qualitative order of convergence, when functions belonging to suitable Lipschitz classes are considered.