Quantitative estimates for Durrmeyer-sampling series in Orlicz spaces

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